多面体上の経路を数える

多面体の頂点から頂点へ辺に沿った経路を数える。遠回りして良いが、同じ頂点を二度通ってはならない。

正四面体

正四面体
始点	終点	最短経路の長さ	経路の個数
$(1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	0	1
$(1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(1 ⁄ \sqrt{2}, - 1 ⁄ \sqrt{2}, - 1 ⁄ \sqrt{2})$	1	5
$(1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(- 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, - 1 ⁄ \sqrt{2})$	1	5
$(1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(- 1 ⁄ \sqrt{2}, - 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	1	5

立方体

立方体
始点	終点	最短経路の長さ	経路の個数
$(1, 1, 1)$	$(1, 1, 1)$	0	1
$(1, 1, 1)$	$(1, 1, - 1)$	1	15
$(1, 1, 1)$	$(1, - 1, 1)$	1	15
$(1, 1, 1)$	$(- 1, 1, 1)$	1	15
$(1, 1, 1)$	$(1, - 1, - 1)$	2	16
$(1, 1, 1)$	$(- 1, 1, - 1)$	2	16
$(1, 1, 1)$	$(- 1, - 1, 1)$	2	16
$(1, 1, 1)$	$(- 1, - 1, - 1)$	3	18

正八面体

正八面体
始点	終点	最短経路の長さ	経路の個数
$(0, 0, \sqrt{2})$	$(0, 0, \sqrt{2})$	0	1
$(0, 0, \sqrt{2})$	$(0, \sqrt{2}, 0)$	1	26
$(0, 0, \sqrt{2})$	$(0, - \sqrt{2}, 0)$	1	26
$(0, 0, \sqrt{2})$	$(\sqrt{2}, 0, 0)$	1	26
$(0, 0, \sqrt{2})$	$(- \sqrt{2}, 0, 0)$	1	26
$(0, 0, \sqrt{2})$	$(0, 0, - \sqrt{2})$	2	28

正十二面体

正十二面体
始点	終点	最短経路の長さ	経路の個数
$(1 + ϕ, 1, 0)$	$(1 + ϕ, 1, 0)$	0	1
$(1 + ϕ, 1, 0)$	$(ϕ, ϕ, ϕ)$	1	561
$(1 + ϕ, 1, 0)$	$(ϕ, ϕ, - ϕ)$	1	561
$(1 + ϕ, 1, 0)$	$(1 + ϕ, - 1, 0)$	1	561
$(1 + ϕ, 1, 0)$	$(0, 1 + ϕ, 1)$	2	589
$(1 + ϕ, 1, 0)$	$(0, 1 + ϕ, - 1)$	2	589
$(1 + ϕ, 1, 0)$	$(1, 0, 1 + ϕ)$	2	589
$(1 + ϕ, 1, 0)$	$(1, 0, - (1 + ϕ))$	2	589
$(1 + ϕ, 1, 0)$	$(ϕ, - ϕ, ϕ)$	2	589
$(1 + ϕ, 1, 0)$	$(ϕ, - ϕ, - ϕ)$	2	589
$(1 + ϕ, 1, 0)$	$(0, - (1 + ϕ), 1)$	3	716
$(1 + ϕ, 1, 0)$	$(0, - (1 + ϕ), - 1)$	3	716
$(1 + ϕ, 1, 0)$	$(- 1, 0, 1 + ϕ)$	3	716
$(1 + ϕ, 1, 0)$	$(- 1, 0, - (1 + ϕ))$	3	716
$(1 + ϕ, 1, 0)$	$(- ϕ, ϕ, ϕ)$	3	716
$(1 + ϕ, 1, 0)$	$(- ϕ, ϕ, - ϕ)$	3	716
$(1 + ϕ, 1, 0)$	$(- ϕ, - ϕ, ϕ)$	4	748
$(1 + ϕ, 1, 0)$	$(- ϕ, - ϕ, - ϕ)$	4	748
$(1 + ϕ, 1, 0)$	$(- (1 + ϕ), 1, 0)$	4	748
$(1 + ϕ, 1, 0)$	$(- (1 + ϕ), - 1, 0)$	5	780

正二十面体

正二十面体
始点	終点	最短経路の長さ	経路の個数
$(0, 1, ϕ)$	$(0, 1, ϕ)$	0	1
$(0, 1, ϕ)$	$(0, - 1, ϕ)$	1	4151
$(0, 1, ϕ)$	$(1, ϕ, 0)$	1	4151
$(0, 1, ϕ)$	$(- 1, ϕ, 0)$	1	4151
$(0, 1, ϕ)$	$(ϕ, 0, 1)$	1	4151
$(0, 1, ϕ)$	$(- ϕ, 0, 1)$	1	4151
$(0, 1, ϕ)$	$(0, 1, - ϕ)$	2	4734
$(0, 1, ϕ)$	$(1, - ϕ, 0)$	2	4734
$(0, 1, ϕ)$	$(- 1, - ϕ, 0)$	2	4734
$(0, 1, ϕ)$	$(ϕ, 0, - 1)$	2	4734
$(0, 1, ϕ)$	$(- ϕ, 0, - 1)$	2	4734
$(0, 1, ϕ)$	$(0, - 1, - ϕ)$	3	5170

切頂四面体

切頂四面体
始点	終点	最短経路の長さ	経路の個数
$(3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	0	1
$(3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 3 ⁄ \sqrt{2})$	1	38
$(3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(1 ⁄ \sqrt{2}, 3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	1	38
$(3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(3 ⁄ \sqrt{2}, - 1 ⁄ \sqrt{2}, - 1 ⁄ \sqrt{2})$	1	49
$(3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(1 ⁄ \sqrt{2}, - 1 ⁄ \sqrt{2}, - 3 ⁄ \sqrt{2})$	2	46
$(3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(1 ⁄ \sqrt{2}, - 3 ⁄ \sqrt{2}, - 1 ⁄ \sqrt{2})$	2	46
$(3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(- 1 ⁄ \sqrt{2}, - 1 ⁄ \sqrt{2}, 3 ⁄ \sqrt{2})$	2	46
$(3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(- 1 ⁄ \sqrt{2}, 3 ⁄ \sqrt{2}, - 1 ⁄ \sqrt{2})$	2	46
$(3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(- 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, - 3 ⁄ \sqrt{2})$	3	46
$(3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(- 1 ⁄ \sqrt{2}, - 3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	3	46
$(3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(- 3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, - 1 ⁄ \sqrt{2})$	3	52
$(3 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	$(- 3 ⁄ \sqrt{2}, - 1 ⁄ \sqrt{2}, 1 ⁄ \sqrt{2})$	3	52

切頂立方体

切頂立方体
始点	終点	最短経路の長さ	経路の個数
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	0	1
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(1 + \sqrt{2}, 1, 1 + \sqrt{2})$	1	1178
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(1 + \sqrt{2}, 1 + \sqrt{2}, 1)$	1	1178
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(- 1, 1 + \sqrt{2}, 1 + \sqrt{2})$	1	1569
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(1 + \sqrt{2}, - 1, 1 + \sqrt{2})$	2	1426
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(1 + \sqrt{2}, 1 + \sqrt{2}, - 1)$	2	1426
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(- (1 + \sqrt{2}), 1, 1 + \sqrt{2})$	2	1426
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(- (1 + \sqrt{2}), 1 + \sqrt{2}, 1)$	2	1426
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(1, 1 + \sqrt{2}, - (1 + \sqrt{2}))$	3	1352
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(1, - (1 + \sqrt{2}), 1 + \sqrt{2})$	3	1352
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(- (1 + \sqrt{2}), - 1, 1 + \sqrt{2})$	3	1386
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(- (1 + \sqrt{2}), 1 + \sqrt{2}, - 1)$	3	1386
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(1 + \sqrt{2}, 1, - (1 + \sqrt{2}))$	3	1524
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(1 + \sqrt{2}, - (1 + \sqrt{2}), 1)$	3	1524
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(- 1, 1 + \sqrt{2}, - (1 + \sqrt{2}))$	4	1352
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(- 1, - (1 + \sqrt{2}), 1 + \sqrt{2})$	4	1352
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(1 + \sqrt{2}, - 1, - (1 + \sqrt{2}))$	4	1652
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(1 + \sqrt{2}, - (1 + \sqrt{2}), - 1)$	4	1652
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(- (1 + \sqrt{2}), 1, - (1 + \sqrt{2}))$	4	1652
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(- (1 + \sqrt{2}), - (1 + \sqrt{2}), 1)$	4	1652
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(1, - (1 + \sqrt{2}), - (1 + \sqrt{2}))$	5	1760
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(- (1 + \sqrt{2}), - 1, - (1 + \sqrt{2}))$	5	1924
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(- (1 + \sqrt{2}), - (1 + \sqrt{2}), - 1)$	5	1924
$(1, 1 + \sqrt{2}, 1 + \sqrt{2})$	$(- 1, - (1 + \sqrt{2}), - (1 + \sqrt{2}))$	6	1888

切頂八面体

切頂八面体
始点	終点	最短経路の長さ	経路の個数
$(0, \sqrt{2}, 2 \sqrt{2})$	$(0, \sqrt{2}, 2 \sqrt{2})$	0	1
$(0, \sqrt{2}, 2 \sqrt{2})$	$(\sqrt{2}, 0, 2 \sqrt{2})$	1	1738
$(0, \sqrt{2}, 2 \sqrt{2})$	$(- \sqrt{2}, 0, 2 \sqrt{2})$	1	1738
$(0, \sqrt{2}, 2 \sqrt{2})$	$(0, 2 \sqrt{2}, \sqrt{2})$	1	1953
$(0, \sqrt{2}, 2 \sqrt{2})$	$(0, - \sqrt{2}, 2 \sqrt{2})$	2	1786
$(0, \sqrt{2}, 2 \sqrt{2})$	$(\sqrt{2}, 2 \sqrt{2}, 0)$	2	1930
$(0, \sqrt{2}, 2 \sqrt{2})$	$(- \sqrt{2}, 2 \sqrt{2}, 0)$	2	1930
$(0, \sqrt{2}, 2 \sqrt{2})$	$(2 \sqrt{2}, 0, \sqrt{2})$	2	1930
$(0, \sqrt{2}, 2 \sqrt{2})$	$(- 2 \sqrt{2}, 0, \sqrt{2})$	2	1930
$(0, \sqrt{2}, 2 \sqrt{2})$	$(2 \sqrt{2}, \sqrt{2}, 0)$	3	1957
$(0, \sqrt{2}, 2 \sqrt{2})$	$(- 2 \sqrt{2}, \sqrt{2}, 0)$	3	1957
$(0, \sqrt{2}, 2 \sqrt{2})$	$(2 \sqrt{2}, - \sqrt{2}, 0)$	3	2281
$(0, \sqrt{2}, 2 \sqrt{2})$	$(- 2 \sqrt{2}, - \sqrt{2}, 0)$	3	2281
$(0, \sqrt{2}, 2 \sqrt{2})$	$(0, 2 \sqrt{2}, - \sqrt{2})$	3	2286
$(0, \sqrt{2}, 2 \sqrt{2})$	$(0, - 2 \sqrt{2}, \sqrt{2})$	3	2286
$(0, \sqrt{2}, 2 \sqrt{2})$	$(\sqrt{2}, - 2 \sqrt{2}, 0)$	4	2392
$(0, \sqrt{2}, 2 \sqrt{2})$	$(- \sqrt{2}, - 2 \sqrt{2}, 0)$	4	2392
$(0, \sqrt{2}, 2 \sqrt{2})$	$(2 \sqrt{2}, 0, - \sqrt{2})$	4	2392
$(0, \sqrt{2}, 2 \sqrt{2})$	$(- 2 \sqrt{2}, 0, - \sqrt{2})$	4	2392
$(0, \sqrt{2}, 2 \sqrt{2})$	$(0, \sqrt{2}, - 2 \sqrt{2})$	4	2450
$(0, \sqrt{2}, 2 \sqrt{2})$	$(0, - 2 \sqrt{2}, - \sqrt{2})$	5	2528
$(0, \sqrt{2}, 2 \sqrt{2})$	$(\sqrt{2}, 0, - 2 \sqrt{2})$	5	2528
$(0, \sqrt{2}, 2 \sqrt{2})$	$(- \sqrt{2}, 0, - 2 \sqrt{2})$	5	2528
$(0, \sqrt{2}, 2 \sqrt{2})$	$(0, - \sqrt{2}, - 2 \sqrt{2})$	6	2568

切頂十二面体

切頂十二面体
始点	終点	最短経路の長さ	経路の個数
$(0, 1, 1 + 3 ϕ)$	$(0, 1, 1 + 3 ϕ)$	0	1
$(0, 1, 1 + 3 ϕ)$	$(1, 1 + ϕ, 2 + 2 ϕ)$	1	47057714
$(0, 1, 1 + 3 ϕ)$	$(- 1, 1 + ϕ, 2 + 2 ϕ)$	1	47057714
$(0, 1, 1 + 3 ϕ)$	$(0, - 1, 1 + 3 ϕ)$	1	62743617
$(0, 1, 1 + 3 ϕ)$	$(1, - (1 + ϕ), 2 + 2 ϕ)$	2	56894466
$(0, 1, 1 + 3 ϕ)$	$(- 1, - (1 + ϕ), 2 + 2 ϕ)$	2	56894466
$(0, 1, 1 + 3 ϕ)$	$(1 + ϕ, 2 ϕ, 1 + 2 ϕ)$	2	56894466
$(0, 1, 1 + 3 ϕ)$	$(- (1 + ϕ), 2 ϕ, 1 + 2 ϕ)$	2	56894466
$(0, 1, 1 + 3 ϕ)$	$(1 + 2 ϕ, 1 + ϕ, 2 ϕ)$	3	54666092
$(0, 1, 1 + 3 ϕ)$	$(- (1 + 2 ϕ), 1 + ϕ, 2 ϕ)$	3	54666092
$(0, 1, 1 + 3 ϕ)$	$(1 + ϕ, - 2 ϕ, 1 + 2 ϕ)$	3	55032914
$(0, 1, 1 + 3 ϕ)$	$(- (1 + ϕ), - 2 ϕ, 1 + 2 ϕ)$	3	55032914
$(0, 1, 1 + 3 ϕ)$	$(2 ϕ, 1 + 2 ϕ, 1 + ϕ)$	3	61363236
$(0, 1, 1 + 3 ϕ)$	$(- 2 ϕ, 1 + 2 ϕ, 1 + ϕ)$	3	61363236
$(0, 1, 1 + 3 ϕ)$	$(1 + 2 ϕ, - (1 + ϕ), 2 ϕ)$	4	55129164
$(0, 1, 1 + 3 ϕ)$	$(- (1 + 2 ϕ), - (1 + ϕ), 2 ϕ)$	4	55129164
$(0, 1, 1 + 3 ϕ)$	$(2 + 2 ϕ, 1, 1 + ϕ)$	4	55129164
$(0, 1, 1 + 3 ϕ)$	$(- (2 + 2 ϕ), 1, 1 + ϕ)$	4	55129164
$(0, 1, 1 + 3 ϕ)$	$(1 + ϕ, 2 + 2 ϕ, 1)$	4	67019012
$(0, 1, 1 + 3 ϕ)$	$(- (1 + ϕ), 2 + 2 ϕ, 1)$	4	67019012
$(0, 1, 1 + 3 ϕ)$	$(2 ϕ, - (1 + 2 ϕ), 1 + ϕ)$	4	67019012
$(0, 1, 1 + 3 ϕ)$	$(- 2 ϕ, - (1 + 2 ϕ), 1 + ϕ)$	4	67019012
$(0, 1, 1 + 3 ϕ)$	$(2 + 2 ϕ, - 1, 1 + ϕ)$	5	55480876
$(0, 1, 1 + 3 ϕ)$	$(- (2 + 2 ϕ), - 1, 1 + ϕ)$	5	55480876
$(0, 1, 1 + 3 ϕ)$	$(1, 1 + 3 ϕ, 0)$	5	66187664
$(0, 1, 1 + 3 ϕ)$	$(- 1, 1 + 3 ϕ, 0)$	5	66187664
$(0, 1, 1 + 3 ϕ)$	$(1 + 3 ϕ, 0, 1)$	5	66187664
$(0, 1, 1 + 3 ϕ)$	$(- (1 + 3 ϕ), 0, 1)$	5	66187664
$(0, 1, 1 + 3 ϕ)$	$(1 + ϕ, 2 + 2 ϕ, - 1)$	5	72076856
$(0, 1, 1 + 3 ϕ)$	$(- (1 + ϕ), 2 + 2 ϕ, - 1)$	5	72076856
$(0, 1, 1 + 3 ϕ)$	$(1 + ϕ, - (2 + 2 ϕ), 1)$	5	79030564
$(0, 1, 1 + 3 ϕ)$	$(- (1 + ϕ), - (2 + 2 ϕ), 1)$	5	79030564
$(0, 1, 1 + 3 ϕ)$	$(1, - (1 + 3 ϕ), 0)$	6	77943568
$(0, 1, 1 + 3 ϕ)$	$(- 1, - (1 + 3 ϕ), 0)$	6	77943568
$(0, 1, 1 + 3 ϕ)$	$(1 + 3 ϕ, 0, - 1)$	6	77943568
$(0, 1, 1 + 3 ϕ)$	$(- (1 + 3 ϕ), 0, - 1)$	6	77943568
$(0, 1, 1 + 3 ϕ)$	$(1 + ϕ, - (2 + 2 ϕ), - 1)$	6	78185464
$(0, 1, 1 + 3 ϕ)$	$(- (1 + ϕ), - (2 + 2 ϕ), - 1)$	6	78185464
$(0, 1, 1 + 3 ϕ)$	$(2 ϕ, 1 + 2 ϕ, - (1 + ϕ))$	6	78185464
$(0, 1, 1 + 3 ϕ)$	$(- 2 ϕ, 1 + 2 ϕ, - (1 + ϕ))$	6	78185464
$(0, 1, 1 + 3 ϕ)$	$(2 + 2 ϕ, 1, - (1 + ϕ))$	7	78208304
$(0, 1, 1 + 3 ϕ)$	$(- (2 + 2 ϕ), 1, - (1 + ϕ))$	7	78208304
$(0, 1, 1 + 3 ϕ)$	$(2 ϕ, - (1 + 2 ϕ), - (1 + ϕ))$	7	78486456
$(0, 1, 1 + 3 ϕ)$	$(- 2 ϕ, - (1 + 2 ϕ), - (1 + ϕ))$	7	78486456
$(0, 1, 1 + 3 ϕ)$	$(1 + 2 ϕ, 1 + ϕ, - 2 ϕ)$	7	78564272
$(0, 1, 1 + 3 ϕ)$	$(- (1 + 2 ϕ), 1 + ϕ, - 2 ϕ)$	7	78564272
$(0, 1, 1 + 3 ϕ)$	$(2 + 2 ϕ, - 1, - (1 + ϕ))$	7	78564272
$(0, 1, 1 + 3 ϕ)$	$(- (2 + 2 ϕ), - 1, - (1 + ϕ))$	7	78564272
$(0, 1, 1 + 3 ϕ)$	$(1 + ϕ, 2 ϕ, - (1 + 2 ϕ))$	7	79777104
$(0, 1, 1 + 3 ϕ)$	$(- (1 + ϕ), 2 ϕ, - (1 + 2 ϕ))$	7	79777104
$(0, 1, 1 + 3 ϕ)$	$(1 + 2 ϕ, - (1 + ϕ), - 2 ϕ)$	8	78961200
$(0, 1, 1 + 3 ϕ)$	$(- (1 + 2 ϕ), - (1 + ϕ), - 2 ϕ)$	8	78961200
$(0, 1, 1 + 3 ϕ)$	$(1, 1 + ϕ, - (2 + 2 ϕ))$	8	81188304
$(0, 1, 1 + 3 ϕ)$	$(- 1, 1 + ϕ, - (2 + 2 ϕ))$	8	81188304
$(0, 1, 1 + 3 ϕ)$	$(1 + ϕ, - 2 ϕ, - (1 + 2 ϕ))$	8	81188304
$(0, 1, 1 + 3 ϕ)$	$(- (1 + ϕ), - 2 ϕ, - (1 + 2 ϕ))$	8	81188304
$(0, 1, 1 + 3 ϕ)$	$(0, 1, - (1 + 3 ϕ))$	9	81615744
$(0, 1, 1 + 3 ϕ)$	$(1, - (1 + ϕ), - (2 + 2 ϕ))$	9	84182608
$(0, 1, 1 + 3 ϕ)$	$(- 1, - (1 + ϕ), - (2 + 2 ϕ))$	9	84182608
$(0, 1, 1 + 3 ϕ)$	$(0, - 1, - (1 + 3 ϕ))$	10	83250048

切頂二十面体

切頂二十面体
始点	終点	最短経路の長さ	経路の個数
$(0, 1, 3 ϕ)$	$(0, 1, 3 ϕ)$	0	1
$(0, 1, 3 ϕ)$	$(ϕ, 2, 1 + 2 ϕ)$	1	181045596
$(0, 1, 3 ϕ)$	$(- ϕ, 2, 1 + 2 ϕ)$	1	181045596
$(0, 1, 3 ϕ)$	$(0, - 1, 3 ϕ)$	1	188580177
$(0, 1, 3 ϕ)$	$(1, 1 + ϕ, 2 ϕ)$	2	184276860
$(0, 1, 3 ϕ)$	$(- 1, 1 + ϕ, 2 ϕ)$	2	184276860
$(0, 1, 3 ϕ)$	$(ϕ, - 2, 1 + 2 ϕ)$	2	189426642
$(0, 1, 3 ϕ)$	$(- ϕ, - 2, 1 + 2 ϕ)$	2	189426642
$(0, 1, 3 ϕ)$	$(2 ϕ, 1, 1 + ϕ)$	2	189426642
$(0, 1, 3 ϕ)$	$(- 2 ϕ, 1, 1 + ϕ)$	2	189426642
$(0, 1, 3 ϕ)$	$(2 ϕ, - 1, 1 + ϕ)$	3	193247271
$(0, 1, 3 ϕ)$	$(- 2 ϕ, - 1, 1 + ϕ)$	3	193247271
$(0, 1, 3 ϕ)$	$(1 + 2 ϕ, ϕ, 2)$	3	234224691
$(0, 1, 3 ϕ)$	$(- (1 + 2 ϕ), ϕ, 2)$	3	234224691
$(0, 1, 3 ϕ)$	$(1, - (1 + ϕ), 2 ϕ)$	3	235220532
$(0, 1, 3 ϕ)$	$(- 1, - (1 + ϕ), 2 ϕ)$	3	235220532
$(0, 1, 3 ϕ)$	$(2, 1 + 2 ϕ, ϕ)$	3	235220532
$(0, 1, 3 ϕ)$	$(- 2, 1 + 2 ϕ, ϕ)$	3	235220532
$(0, 1, 3 ϕ)$	$(1 + ϕ, 2 ϕ, 1)$	4	244920498
$(0, 1, 3 ϕ)$	$(- (1 + ϕ), 2 ϕ, 1)$	4	244920498
$(0, 1, 3 ϕ)$	$(1 + 2 ϕ, - ϕ, 2)$	4	244920498
$(0, 1, 3 ϕ)$	$(- (1 + 2 ϕ), - ϕ, 2)$	4	244920498
$(0, 1, 3 ϕ)$	$(1, 3 ϕ, 0)$	4	252346876
$(0, 1, 3 ϕ)$	$(- 1, 3 ϕ, 0)$	4	252346876
$(0, 1, 3 ϕ)$	$(3 ϕ, 0, 1)$	4	252346876
$(0, 1, 3 ϕ)$	$(- 3 ϕ, 0, 1)$	4	252346876
$(0, 1, 3 ϕ)$	$(2, - (1 + 2 ϕ), ϕ)$	4	256478193
$(0, 1, 3 ϕ)$	$(- 2, - (1 + 2 ϕ), ϕ)$	4	256478193
$(0, 1, 3 ϕ)$	$(1 + ϕ, - 2 ϕ, 1)$	5	260517095
$(0, 1, 3 ϕ)$	$(- (1 + ϕ), - 2 ϕ, 1)$	5	260517095
$(0, 1, 3 ϕ)$	$(1 + ϕ, 2 ϕ, - 1)$	5	271076863
$(0, 1, 3 ϕ)$	$(- (1 + ϕ), 2 ϕ, - 1)$	5	271076863
$(0, 1, 3 ϕ)$	$(2, 1 + 2 ϕ, - ϕ)$	5	275722873
$(0, 1, 3 ϕ)$	$(- 2, 1 + 2 ϕ, - ϕ)$	5	275722873
$(0, 1, 3 ϕ)$	$(1, - 3 ϕ, 0)$	5	277249526
$(0, 1, 3 ϕ)$	$(- 1, - 3 ϕ, 0)$	5	277249526
$(0, 1, 3 ϕ)$	$(3 ϕ, 0, - 1)$	5	277249526
$(0, 1, 3 ϕ)$	$(- 3 ϕ, 0, - 1)$	5	277249526
$(0, 1, 3 ϕ)$	$(1 + ϕ, - 2 ϕ, - 1)$	6	282478161
$(0, 1, 3 ϕ)$	$(- (1 + ϕ), - 2 ϕ, - 1)$	6	282478161
$(0, 1, 3 ϕ)$	$(1 + 2 ϕ, ϕ, - 2)$	6	282478161
$(0, 1, 3 ϕ)$	$(- (1 + 2 ϕ), ϕ, - 2)$	6	282478161
$(0, 1, 3 ϕ)$	$(1 + 2 ϕ, - ϕ, - 2)$	6	287452904
$(0, 1, 3 ϕ)$	$(- (1 + 2 ϕ), - ϕ, - 2)$	6	287452904
$(0, 1, 3 ϕ)$	$(1, 1 + ϕ, - 2 ϕ)$	6	289570721
$(0, 1, 3 ϕ)$	$(- 1, 1 + ϕ, - 2 ϕ)$	6	289570721
$(0, 1, 3 ϕ)$	$(2, - (1 + 2 ϕ), - ϕ)$	6	289570721
$(0, 1, 3 ϕ)$	$(- 2, - (1 + 2 ϕ), - ϕ)$	6	289570721
$(0, 1, 3 ϕ)$	$(2 ϕ, 1, - (1 + ϕ))$	7	296817377
$(0, 1, 3 ϕ)$	$(- 2 ϕ, 1, - (1 + ϕ))$	7	296817377
$(0, 1, 3 ϕ)$	$(ϕ, 2, - (1 + 2 ϕ))$	7	299650106
$(0, 1, 3 ϕ)$	$(- ϕ, 2, - (1 + 2 ϕ))$	7	299650106
$(0, 1, 3 ϕ)$	$(2 ϕ, - 1, - (1 + ϕ))$	7	299650106
$(0, 1, 3 ϕ)$	$(- 2 ϕ, - 1, - (1 + ϕ))$	7	299650106
$(0, 1, 3 ϕ)$	$(1, - (1 + ϕ), - 2 ϕ)$	7	300511689
$(0, 1, 3 ϕ)$	$(- 1, - (1 + ϕ), - 2 ϕ)$	7	300511689
$(0, 1, 3 ϕ)$	$(ϕ, - 2, - (1 + 2 ϕ))$	8	304740008
$(0, 1, 3 ϕ)$	$(- ϕ, - 2, - (1 + 2 ϕ))$	8	304740008
$(0, 1, 3 ϕ)$	$(0, 1, - 3 ϕ)$	8	305057930
$(0, 1, 3 ϕ)$	$(0, - 1, - 3 ϕ)$	9	307611158

立方八面体

立方八面体
始点	終点	最短経路の長さ	経路の個数
$(0, \sqrt{2}, \sqrt{2})$	$(0, \sqrt{2}, \sqrt{2})$	0	1
$(0, \sqrt{2}, \sqrt{2})$	$(\sqrt{2}, 0, \sqrt{2})$	1	546
$(0, \sqrt{2}, \sqrt{2})$	$(\sqrt{2}, \sqrt{2}, 0)$	1	546
$(0, \sqrt{2}, \sqrt{2})$	$(- \sqrt{2}, 0, \sqrt{2})$	1	546
$(0, \sqrt{2}, \sqrt{2})$	$(- \sqrt{2}, \sqrt{2}, 0)$	1	546
$(0, \sqrt{2}, \sqrt{2})$	$(0, \sqrt{2}, - \sqrt{2})$	2	590
$(0, \sqrt{2}, \sqrt{2})$	$(0, - \sqrt{2}, \sqrt{2})$	2	590
$(0, \sqrt{2}, \sqrt{2})$	$(\sqrt{2}, 0, - \sqrt{2})$	2	644
$(0, \sqrt{2}, \sqrt{2})$	$(\sqrt{2}, - \sqrt{2}, 0)$	2	644
$(0, \sqrt{2}, \sqrt{2})$	$(- \sqrt{2}, 0, - \sqrt{2})$	2	644
$(0, \sqrt{2}, \sqrt{2})$	$(- \sqrt{2}, - \sqrt{2}, 0)$	2	644
$(0, \sqrt{2}, \sqrt{2})$	$(0, - \sqrt{2}, - \sqrt{2})$	3	684

二十面十二面体

二十面十二面体
始点	終点	最短経路の長さ	経路の個数
$(2 ϕ, 0, 0)$	$(2 ϕ, 0, 0)$	0	1
$(2 ϕ, 0, 0)$	$(1 + ϕ, ϕ, 1)$	1	7545354
$(2 ϕ, 0, 0)$	$(1 + ϕ, ϕ, - 1)$	1	7545354
$(2 ϕ, 0, 0)$	$(1 + ϕ, - ϕ, 1)$	1	7545354
$(2 ϕ, 0, 0)$	$(1 + ϕ, - ϕ, - 1)$	1	7545354
$(2 ϕ, 0, 0)$	$(ϕ, 1, 1 + ϕ)$	2	7965296
$(2 ϕ, 0, 0)$	$(ϕ, 1, - (1 + ϕ))$	2	7965296
$(2 ϕ, 0, 0)$	$(ϕ, - 1, 1 + ϕ)$	2	7965296
$(2 ϕ, 0, 0)$	$(ϕ, - 1, - (1 + ϕ))$	2	7965296
$(2 ϕ, 0, 0)$	$(1, 1 + ϕ, ϕ)$	2	9037068
$(2 ϕ, 0, 0)$	$(1, 1 + ϕ, - ϕ)$	2	9037068
$(2 ϕ, 0, 0)$	$(1, - (1 + ϕ), ϕ)$	2	9037068
$(2 ϕ, 0, 0)$	$(1, - (1 + ϕ), - ϕ)$	2	9037068
$(2 ϕ, 0, 0)$	$(0, 0, 2 ϕ)$	3	9744392
$(2 ϕ, 0, 0)$	$(0, 0, - 2 ϕ)$	3	9744392
$(2 ϕ, 0, 0)$	$(0, 2 ϕ, 0)$	3	9744392
$(2 ϕ, 0, 0)$	$(0, - 2 ϕ, 0)$	3	9744392
$(2 ϕ, 0, 0)$	$(- 1, 1 + ϕ, ϕ)$	3	10414664
$(2 ϕ, 0, 0)$	$(- 1, 1 + ϕ, - ϕ)$	3	10414664
$(2 ϕ, 0, 0)$	$(- 1, - (1 + ϕ), ϕ)$	3	10414664
$(2 ϕ, 0, 0)$	$(- 1, - (1 + ϕ), - ϕ)$	3	10414664
$(2 ϕ, 0, 0)$	$(- ϕ, 1, 1 + ϕ)$	4	10850870
$(2 ϕ, 0, 0)$	$(- ϕ, 1, - (1 + ϕ))$	4	10850870
$(2 ϕ, 0, 0)$	$(- ϕ, - 1, 1 + ϕ)$	4	10850870
$(2 ϕ, 0, 0)$	$(- ϕ, - 1, - (1 + ϕ))$	4	10850870
$(2 ϕ, 0, 0)$	$(- (1 + ϕ), ϕ, 1)$	4	11201450
$(2 ϕ, 0, 0)$	$(- (1 + ϕ), ϕ, - 1)$	4	11201450
$(2 ϕ, 0, 0)$	$(- (1 + ϕ), - ϕ, 1)$	4	11201450
$(2 ϕ, 0, 0)$	$(- (1 + ϕ), - ϕ, - 1)$	4	11201450
$(2 ϕ, 0, 0)$	$(- 2 ϕ, 0, 0)$	5	11461272

小斜方立方八面体

小斜方立方八面体
始点	終点	最短経路の長さ	経路の個数
$(1, 1, 1 + \sqrt{2})$	$(1, 1, 1 + \sqrt{2})$	0	1
$(1, 1, 1 + \sqrt{2})$	$(1, 1 + \sqrt{2}, 1)$	1	315050
$(1, 1, 1 + \sqrt{2})$	$(1 + \sqrt{2}, 1, 1)$	1	315050
$(1, 1, 1 + \sqrt{2})$	$(1, - 1, 1 + \sqrt{2})$	1	345326
$(1, 1, 1 + \sqrt{2})$	$(- 1, 1, 1 + \sqrt{2})$	1	345326
$(1, 1, 1 + \sqrt{2})$	$(- 1, - 1, 1 + \sqrt{2})$	2	339702
$(1, 1, 1 + \sqrt{2})$	$(- 1, 1 + \sqrt{2}, 1)$	2	342876
$(1, 1, 1 + \sqrt{2})$	$(1 + \sqrt{2}, - 1, 1)$	2	342876
$(1, 1, 1 + \sqrt{2})$	$(1, 1 + \sqrt{2}, - 1)$	2	387506
$(1, 1, 1 + \sqrt{2})$	$(1, - (1 + \sqrt{2}), 1)$	2	387506
$(1, 1, 1 + \sqrt{2})$	$(1 + \sqrt{2}, 1, - 1)$	2	387506
$(1, 1, 1 + \sqrt{2})$	$(- (1 + \sqrt{2}), 1, 1)$	2	387506
$(1, 1, 1 + \sqrt{2})$	$(- 1, 1 + \sqrt{2}, - 1)$	3	422254
$(1, 1, 1 + \sqrt{2})$	$(- 1, - (1 + \sqrt{2}), 1)$	3	422254
$(1, 1, 1 + \sqrt{2})$	$(1 + \sqrt{2}, - 1, - 1)$	3	422254
$(1, 1, 1 + \sqrt{2})$	$(- (1 + \sqrt{2}), - 1, 1)$	3	422254
$(1, 1, 1 + \sqrt{2})$	$(1, 1, - (1 + \sqrt{2}))$	3	431496
$(1, 1, 1 + \sqrt{2})$	$(1, - (1 + \sqrt{2}), - 1)$	3	449648
$(1, 1, 1 + \sqrt{2})$	$(- (1 + \sqrt{2}), 1, - 1)$	3	449648
$(1, 1, 1 + \sqrt{2})$	$(1, - 1, - (1 + \sqrt{2}))$	4	459844
$(1, 1, 1 + \sqrt{2})$	$(- 1, 1, - (1 + \sqrt{2}))$	4	459844
$(1, 1, 1 + \sqrt{2})$	$(- 1, - (1 + \sqrt{2}), - 1)$	4	474458
$(1, 1, 1 + \sqrt{2})$	$(- (1 + \sqrt{2}), - 1, - 1)$	4	474458
$(1, 1, 1 + \sqrt{2})$	$(- 1, - 1, - (1 + \sqrt{2}))$	5	484088

小斜方二十面十二面体

小斜方二十面十二面体
始点	終点	最短経路の長さ	経路の個数
$(1, 1, 1 + 2 ϕ)$	$(1, 1, 1 + 2 ϕ)$	0	1
$(1, 1, 1 + 2 ϕ)$	$(0, 1 + ϕ, 1 + ϕ)$	1	89202613227098
$(1, 1, 1 + 2 ϕ)$	$(- 1, 1, 1 + 2 ϕ)$	1	89202613227098
$(1, 1, 1 + 2 ϕ)$	$(1, - 1, 1 + 2 ϕ)$	1	101218512140962
$(1, 1, 1 + 2 ϕ)$	$(1 + ϕ, ϕ, 2 ϕ)$	1	101218512140962
$(1, 1, 1 + 2 ϕ)$	$(- 1, - 1, 1 + 2 ϕ)$	2	98007796804202
$(1, 1, 1 + 2 ϕ)$	$(ϕ, 2 ϕ, 1 + ϕ)$	2	98007796804202
$(1, 1, 1 + 2 ϕ)$	$(1 + ϕ, - ϕ, 2 ϕ)$	2	100170874303270
$(1, 1, 1 + 2 ϕ)$	$(1 + ϕ, 0, 1 + ϕ)$	2	100170874303270
$(1, 1, 1 + 2 ϕ)$	$(0, - (1 + ϕ), 1 + ϕ)$	2	111575227090816
$(1, 1, 1 + 2 ϕ)$	$(- ϕ, 2 ϕ, 1 + ϕ)$	2	111575227090816
$(1, 1, 1 + 2 ϕ)$	$(- (1 + ϕ), ϕ, 2 ϕ)$	2	111575227090816
$(1, 1, 1 + 2 ϕ)$	$(2 ϕ, 1 + ϕ, ϕ)$	2	111575227090816
$(1, 1, 1 + 2 ϕ)$	$(1, 1 + 2 ϕ, 1)$	3	123777113936048
$(1, 1, 1 + 2 ϕ)$	$(ϕ, - 2 ϕ, 1 + ϕ)$	3	123777113936048
$(1, 1, 1 + 2 ϕ)$	$(- (1 + ϕ), - ϕ, 2 ϕ)$	3	123777113936048
$(1, 1, 1 + 2 ϕ)$	$(1 + 2 ϕ, 1, 1)$	3	123777113936048
$(1, 1, 1 + 2 ϕ)$	$(- 1, 1 + 2 ϕ, 1)$	3	124948381753436
$(1, 1, 1 + 2 ϕ)$	$(2 ϕ, - (1 + ϕ), ϕ)$	3	124948381753436
$(1, 1, 1 + 2 ϕ)$	$(- (1 + ϕ), 0, 1 + ϕ)$	3	124948381753436
$(1, 1, 1 + 2 ϕ)$	$(1 + 2 ϕ, - 1, 1)$	3	124948381753436
$(1, 1, 1 + 2 ϕ)$	$(- 2 ϕ, 1 + ϕ, ϕ)$	3	125086154372604
$(1, 1, 1 + 2 ϕ)$	$(- ϕ, - 2 ϕ, 1 + ϕ)$	3	132357801949244
$(1, 1, 1 + 2 ϕ)$	$(1 + ϕ, 1 + ϕ, 0)$	3	132357801949244
$(1, 1, 1 + 2 ϕ)$	$(1, 1 + 2 ϕ, - 1)$	4	137877510657448
$(1, 1, 1 + 2 ϕ)$	$(- (1 + ϕ), 1 + ϕ, 0)$	4	137877510657448
$(1, 1, 1 + 2 ϕ)$	$(- 2 ϕ, - (1 + ϕ), ϕ)$	4	137877510657448
$(1, 1, 1 + 2 ϕ)$	$(- (1 + 2 ϕ), 1, 1)$	4	137877510657448
$(1, 1, 1 + 2 ϕ)$	$(- 1, 1 + 2 ϕ, - 1)$	4	139997735860828
$(1, 1, 1 + 2 ϕ)$	$(- (1 + 2 ϕ), - 1, 1)$	4	139997735860828
$(1, 1, 1 + 2 ϕ)$	$(1, - (1 + 2 ϕ), 1)$	4	143173537815020
$(1, 1, 1 + 2 ϕ)$	$(1 + 2 ϕ, 1, - 1)$	4	143173537815020
$(1, 1, 1 + 2 ϕ)$	$(- 1, - (1 + 2 ϕ), 1)$	4	145105722422936
$(1, 1, 1 + 2 ϕ)$	$(1 + ϕ, - (1 + ϕ), 0)$	4	145105722422936
$(1, 1, 1 + 2 ϕ)$	$(2 ϕ, 1 + ϕ, - ϕ)$	4	145105722422936
$(1, 1, 1 + 2 ϕ)$	$(1 + 2 ϕ, - 1, - 1)$	4	145105722422936
$(1, 1, 1 + 2 ϕ)$	$(2 ϕ, - (1 + ϕ), - ϕ)$	5	149550129802328
$(1, 1, 1 + 2 ϕ)$	$(ϕ, 2 ϕ, - (1 + ϕ))$	5	150520223151628
$(1, 1, 1 + 2 ϕ)$	$(- (1 + ϕ), - (1 + ϕ), 0)$	5	150520223151628
$(1, 1, 1 + 2 ϕ)$	$(1, - (1 + 2 ϕ), - 1)$	5	150685170905612
$(1, 1, 1 + 2 ϕ)$	$(- 2 ϕ, 1 + ϕ, - ϕ)$	5	150685170905612
$(1, 1, 1 + 2 ϕ)$	$(1 + ϕ, 0, - (1 + ϕ))$	5	150685170905612
$(1, 1, 1 + 2 ϕ)$	$(- (1 + 2 ϕ), 1, - 1)$	5	150685170905612
$(1, 1, 1 + 2 ϕ)$	$(- 1, - (1 + 2 ϕ), - 1)$	5	153215948615446
$(1, 1, 1 + 2 ϕ)$	$(- ϕ, 2 ϕ, - (1 + ϕ))$	5	153215948615446
$(1, 1, 1 + 2 ϕ)$	$(1 + ϕ, ϕ, - 2 ϕ)$	5	153215948615446
$(1, 1, 1 + 2 ϕ)$	$(- (1 + 2 ϕ), - 1, - 1)$	5	153215948615446
$(1, 1, 1 + 2 ϕ)$	$(0, 1 + ϕ, - (1 + ϕ))$	6	156382970312668
$(1, 1, 1 + 2 ϕ)$	$(ϕ, - 2 ϕ, - (1 + ϕ))$	6	156382970312668
$(1, 1, 1 + 2 ϕ)$	$(1 + ϕ, - ϕ, - 2 ϕ)$	6	156382970312668
$(1, 1, 1 + 2 ϕ)$	$(- 2 ϕ, - (1 + ϕ), - ϕ)$	6	156382970312668
$(1, 1, 1 + 2 ϕ)$	$(- (1 + ϕ), ϕ, - 2 ϕ)$	6	156976120910240
$(1, 1, 1 + 2 ϕ)$	$(- (1 + ϕ), 0, - (1 + ϕ))$	6	156976120910240
$(1, 1, 1 + 2 ϕ)$	$(1, 1, - (1 + 2 ϕ))$	6	159431847518790
$(1, 1, 1 + 2 ϕ)$	$(- ϕ, - 2 ϕ, - (1 + ϕ))$	6	159431847518790
$(1, 1, 1 + 2 ϕ)$	$(- 1, 1, - (1 + 2 ϕ))$	7	160624282004270
$(1, 1, 1 + 2 ϕ)$	$(- (1 + ϕ), - ϕ, - 2 ϕ)$	7	160624282004270
$(1, 1, 1 + 2 ϕ)$	$(0, - (1 + ϕ), - (1 + ϕ))$	7	161489778486404
$(1, 1, 1 + 2 ϕ)$	$(1, - 1, - (1 + 2 ϕ))$	7	161489778486404
$(1, 1, 1 + 2 ϕ)$	$(- 1, - 1, - (1 + 2 ϕ))$	8	162567930895168

大斜方立方八面体

大斜方立方八面体
始点	終点	最短経路の長さ	経路の個数
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	0	1
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1, 1 + 2 \sqrt{2}, 1 + \sqrt{2})$	1	2821146
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- 1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	1	2951002
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + \sqrt{2}, 1, 1 + 2 \sqrt{2})$	1	3291385
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- 1, 1 + 2 \sqrt{2}, 1 + \sqrt{2})$	2	2919482
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + \sqrt{2}, 1 + 2 \sqrt{2}, 1)$	2	3160118
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + 2 \sqrt{2}, 1, 1 + \sqrt{2})$	2	3160118
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + \sqrt{2}, - 1, 1 + 2 \sqrt{2})$	2	3226450
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + \sqrt{2}), 1, 1 + 2 \sqrt{2})$	2	3226450
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + 2 \sqrt{2}, 1 + \sqrt{2}, 1)$	3	3172332
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + \sqrt{2}), - 1, 1 + 2 \sqrt{2})$	3	3335866
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1, - (1 + \sqrt{2}), 1 + 2 \sqrt{2})$	3	3355572
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + \sqrt{2}, 1 + 2 \sqrt{2}, - 1)$	3	3792922
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + 2 \sqrt{2}), 1, 1 + \sqrt{2})$	3	3792922
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + \sqrt{2}), 1 + 2 \sqrt{2}, 1)$	3	3813754
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + 2 \sqrt{2}, - 1, 1 + \sqrt{2})$	3	3813754
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- 1, - (1 + \sqrt{2}), 1 + 2 \sqrt{2})$	4	3401096
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + 2 \sqrt{2}, 1 + \sqrt{2}, - 1)$	4	3993748
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + 2 \sqrt{2}), 1 + \sqrt{2}, 1)$	4	3993748
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + \sqrt{2}), 1 + 2 \sqrt{2}, - 1)$	4	4042592
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + 2 \sqrt{2}), - 1, 1 + \sqrt{2})$	4	4042592
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1, 1 + 2 \sqrt{2}, - (1 + \sqrt{2}))$	4	4115192
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1, - (1 + 2 \sqrt{2}), 1 + \sqrt{2})$	4	4115192
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + 2 \sqrt{2}, - (1 + \sqrt{2}), 1)$	4	4172354
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- 1, 1 + 2 \sqrt{2}, - (1 + \sqrt{2}))$	5	4145894
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- 1, - (1 + 2 \sqrt{2}), 1 + \sqrt{2})$	5	4145894
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + 2 \sqrt{2}), 1 + \sqrt{2}, - 1)$	5	4345588
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + \sqrt{2}, - (1 + 2 \sqrt{2}), 1)$	5	4379756
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + 2 \sqrt{2}, 1, - (1 + \sqrt{2}))$	5	4379756
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + 2 \sqrt{2}, - (1 + \sqrt{2}), - 1)$	5	4414712
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + 2 \sqrt{2}), - (1 + \sqrt{2}), 1)$	5	4414712
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1, 1 + \sqrt{2}, - (1 + 2 \sqrt{2}))$	5	4477970
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + \sqrt{2}), - (1 + 2 \sqrt{2}), 1)$	6	4477504
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + 2 \sqrt{2}, - 1, - (1 + \sqrt{2}))$	6	4477504
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + \sqrt{2}, 1, - (1 + 2 \sqrt{2}))$	6	4568412
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- 1, 1 + \sqrt{2}, - (1 + 2 \sqrt{2}))$	6	4576336
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + \sqrt{2}, - (1 + 2 \sqrt{2}), - 1)$	6	4607476
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + 2 \sqrt{2}), 1, - (1 + \sqrt{2}))$	6	4607476
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + 2 \sqrt{2}), - (1 + \sqrt{2}), - 1)$	6	4661716
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + \sqrt{2}), - (1 + 2 \sqrt{2}), - 1)$	7	4721920
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + 2 \sqrt{2}), - 1, - (1 + \sqrt{2}))$	7	4721920
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1 + \sqrt{2}, - 1, - (1 + 2 \sqrt{2}))$	7	4738096
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + \sqrt{2}), 1, - (1 + 2 \sqrt{2}))$	7	4738096
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1, - (1 + 2 \sqrt{2}), - (1 + \sqrt{2}))$	7	4773740
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- 1, - (1 + 2 \sqrt{2}), - (1 + \sqrt{2}))$	8	4819816
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- (1 + \sqrt{2}), - 1, - (1 + 2 \sqrt{2}))$	8	4848352
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(1, - (1 + \sqrt{2}), - (1 + 2 \sqrt{2}))$	8	4853984
$(1, 1 + \sqrt{2}, 1 + 2 \sqrt{2})$	$(- 1, - (1 + \sqrt{2}), - (1 + 2 \sqrt{2}))$	9	4889088

大斜方二十面十二面体

大斜方二十面十二面体
始点	終点	最短経路の長さ	経路の個数
$(1, 1, 1 + 4 ϕ)$	$(1, 1, 1 + 4 ϕ)$	0	1
$(1, 1, 1 + 4 ϕ)$	$(- 1, 1, 1 + 4 ϕ)$	1	16648953820232074
$(1, 1, 1 + 4 ϕ)$	$(1, - 1, 1 + 4 ϕ)$	1	17761151206070874
$(1, 1, 1 + 4 ϕ)$	$(2, 1 + ϕ, 2 + 3 ϕ)$	1	19735132861167641
$(1, 1, 1 + 4 ϕ)$	$(- 1, - 1, 1 + 4 ϕ)$	2	17303115627360266
$(1, 1, 1 + 4 ϕ)$	$(1, 1 + 2 ϕ, 3 + 2 ϕ)$	2	18716163436978058
$(1, 1, 1 + 4 ϕ)$	$(- 2, 1 + ϕ, 2 + 3 ϕ)$	2	18716163436978058
$(1, 1, 1 + 4 ϕ)$	$(2, - (1 + ϕ), 2 + 3 ϕ)$	2	19312198438142302
$(1, 1, 1 + 4 ϕ)$	$(1 + ϕ, 2 ϕ, 1 + 3 ϕ)$	2	19312198438142302
$(1, 1, 1 + 4 ϕ)$	$(- 1, 1 + 2 ϕ, 3 + 2 ϕ)$	3	18702882291733226
$(1, 1, 1 + 4 ϕ)$	$(1 + ϕ, - 2 ϕ, 1 + 3 ϕ)$	3	20137786588374548
$(1, 1, 1 + 4 ϕ)$	$(2 + 2 ϕ, 1 + ϕ, 3 ϕ)$	3	20321035498308522
$(1, 1, 1 + 4 ϕ)$	$(1, - (1 + 2 ϕ), 3 + 2 ϕ)$	3	22657651660570840
$(1, 1, 1 + 4 ϕ)$	$(- (1 + ϕ), 2 ϕ, 1 + 3 ϕ)$	3	22657651660570840
$(1, 1, 1 + 4 ϕ)$	$(- 2, - (1 + ϕ), 2 + 3 ϕ)$	3	22777475454669278
$(1, 1, 1 + 4 ϕ)$	$(1 + ϕ, 3 ϕ, 2 + 2 ϕ)$	3	22777475454669278
$(1, 1, 1 + 4 ϕ)$	$(2 + 2 ϕ, - (1 + ϕ), 3 ϕ)$	4	20915167841555196
$(1, 1, 1 + 4 ϕ)$	$(3 + 2 ϕ, 1, 1 + 2 ϕ)$	4	20915167841555196
$(1, 1, 1 + 4 ϕ)$	$(- 1, - (1 + 2 ϕ), 3 + 2 ϕ)$	4	23881796948510728
$(1, 1, 1 + 4 ϕ)$	$(- (1 + ϕ), 3 ϕ, 2 + 2 ϕ)$	4	23881796948510728
$(1, 1, 1 + 4 ϕ)$	$(1 + ϕ, - 3 ϕ, 2 + 2 ϕ)$	4	24330551279189436
$(1, 1, 1 + 4 ϕ)$	$(- (1 + ϕ), - 2 ϕ, 1 + 3 ϕ)$	4	24330551279189436
$(1, 1, 1 + 4 ϕ)$	$(- (2 + 2 ϕ), 1 + ϕ, 3 ϕ)$	4	24938977365733016
$(1, 1, 1 + 4 ϕ)$	$(1 + 3 ϕ, 1 + ϕ, 2 ϕ)$	4	24938977365733016
$(1, 1, 1 + 4 ϕ)$	$(2 ϕ, 1 + 3 ϕ, 1 + ϕ)$	4	25106042917475890
$(1, 1, 1 + 4 ϕ)$	$(3 + 2 ϕ, - 1, 1 + 2 ϕ)$	5	21127175551522244
$(1, 1, 1 + 4 ϕ)$	$(- (2 + 2 ϕ), - (1 + ϕ), 3 ϕ)$	5	25422081422918236
$(1, 1, 1 + 4 ϕ)$	$(2 + 3 ϕ, 2, 1 + ϕ)$	5	25422081422918236
$(1, 1, 1 + 4 ϕ)$	$(1 + 3 ϕ, - (1 + ϕ), 2 ϕ)$	5	25585191507373656
$(1, 1, 1 + 4 ϕ)$	$(- (3 + 2 ϕ), 1, 1 + 2 ϕ)$	5	25585191507373656
$(1, 1, 1 + 4 ϕ)$	$(- (1 + ϕ), - 3 ϕ, 2 + 2 ϕ)$	5	26222257502358028
$(1, 1, 1 + 4 ϕ)$	$(- 2 ϕ, 1 + 3 ϕ, 1 + ϕ)$	5	26540206872687912
$(1, 1, 1 + 4 ϕ)$	$(3 ϕ, 2 + 2 ϕ, 1 + ϕ)$	5	26540206872687912
$(1, 1, 1 + 4 ϕ)$	$(1 + ϕ, 2 + 3 ϕ, 2)$	5	26841596599009076
$(1, 1, 1 + 4 ϕ)$	$(2 ϕ, - (1 + 3 ϕ), 1 + ϕ)$	5	26841596599009076
$(1, 1, 1 + 4 ϕ)$	$(- (1 + 3 ϕ), 1 + ϕ, 2 ϕ)$	5	27367058310578352
$(1, 1, 1 + 4 ϕ)$	$(- (3 + 2 ϕ), - 1, 1 + 2 ϕ)$	6	25795683861419096
$(1, 1, 1 + 4 ϕ)$	$(2 + 3 ϕ, - 2, 1 + ϕ)$	6	25795683861419096
$(1, 1, 1 + 4 ϕ)$	$(- (1 + ϕ), 2 + 3 ϕ, 2)$	6	27572174909894296
$(1, 1, 1 + 4 ϕ)$	$(3 ϕ, - (2 + 2 ϕ), 1 + ϕ)$	6	27572174909894296
$(1, 1, 1 + 4 ϕ)$	$(1, 1 + 4 ϕ, 1)$	6	27799272717127964
$(1, 1, 1 + 4 ϕ)$	$(1 + 4 ϕ, 1, 1)$	6	27799272717127964
$(1, 1, 1 + 4 ϕ)$	$(- 3 ϕ, 2 + 2 ϕ, 1 + ϕ)$	6	27905677872968576
$(1, 1, 1 + 4 ϕ)$	$(- 2 ϕ, - (1 + 3 ϕ), 1 + ϕ)$	6	28222595178640836
$(1, 1, 1 + 4 ϕ)$	$(1 + 2 ϕ, 3 + 2 ϕ, 1)$	6	28222595178640836
$(1, 1, 1 + 4 ϕ)$	$(- (1 + 3 ϕ), - (1 + ϕ), 2 ϕ)$	6	28520829391291136
$(1, 1, 1 + 4 ϕ)$	$(- (2 + 3 ϕ), 2, 1 + ϕ)$	6	28520829391291136
$(1, 1, 1 + 4 ϕ)$	$(1 + ϕ, - (2 + 3 ϕ), 2)$	6	28684441584252904
$(1, 1, 1 + 4 ϕ)$	$(- 1, 1 + 4 ϕ, 1)$	7	28024356421526568
$(1, 1, 1 + 4 ϕ)$	$(1 + 4 ϕ, - 1, 1)$	7	28024356421526568
$(1, 1, 1 + 4 ϕ)$	$(- (2 + 3 ϕ), - 2, 1 + ϕ)$	7	28914403809526464
$(1, 1, 1 + 4 ϕ)$	$(- (1 + ϕ), - (2 + 3 ϕ), 2)$	7	29383682344078936
$(1, 1, 1 + 4 ϕ)$	$(1 + 2 ϕ, - (3 + 2 ϕ), 1)$	7	29383682344078936
$(1, 1, 1 + 4 ϕ)$	$(- (1 + 2 ϕ), 3 + 2 ϕ, 1)$	7	29461548639589472
$(1, 1, 1 + 4 ϕ)$	$(- 3 ϕ, - (2 + 2 ϕ), 1 + ϕ)$	7	29461548639589472
$(1, 1, 1 + 4 ϕ)$	$(1, - (1 + 4 ϕ), 1)$	7	29654287525360536
$(1, 1, 1 + 4 ϕ)$	$(1 + 4 ϕ, 1, - 1)$	7	29654287525360536
$(1, 1, 1 + 4 ϕ)$	$(1 + 2 ϕ, 3 + 2 ϕ, - 1)$	7	29758653913563484
$(1, 1, 1 + 4 ϕ)$	$(1, 1 + 4 ϕ, - 1)$	7	30256689882724512
$(1, 1, 1 + 4 ϕ)$	$(- (1 + 4 ϕ), 1, 1)$	7	30256689882724512
$(1, 1, 1 + 4 ϕ)$	$(- 1, - (1 + 4 ϕ), 1)$	8	29848616127374776
$(1, 1, 1 + 4 ϕ)$	$(1 + 4 ϕ, - 1, - 1)$	8	29848616127374776
$(1, 1, 1 + 4 ϕ)$	$(- 1, 1 + 4 ϕ, - 1)$	8	30441902867674648
$(1, 1, 1 + 4 ϕ)$	$(- (1 + 4 ϕ), - 1, 1)$	8	30441902867674648
$(1, 1, 1 + 4 ϕ)$	$(1 + 2 ϕ, - (3 + 2 ϕ), - 1)$	8	30658323317446088
$(1, 1, 1 + 4 ϕ)$	$(3 ϕ, 2 + 2 ϕ, - (1 + ϕ))$	8	30658323317446088
$(1, 1, 1 + 4 ϕ)$	$(2 + 3 ϕ, 2, - (1 + ϕ))$	8	30686986876809000
$(1, 1, 1 + 4 ϕ)$	$(- (1 + 2 ϕ), - (3 + 2 ϕ), 1)$	8	30699967435029640
$(1, 1, 1 + 4 ϕ)$	$(1 + ϕ, 2 + 3 ϕ, - 2)$	8	30931147929141936
$(1, 1, 1 + 4 ϕ)$	$(- (1 + 2 ϕ), 3 + 2 ϕ, - 1)$	8	30931147929141936
$(1, 1, 1 + 4 ϕ)$	$(1, - (1 + 4 ϕ), - 1)$	8	31514183675072384
$(1, 1, 1 + 4 ϕ)$	$(- (1 + 4 ϕ), 1, - 1)$	8	31514183675072384
$(1, 1, 1 + 4 ϕ)$	$(1 + 3 ϕ, 1 + ϕ, - 2 ϕ)$	9	30966310020358744
$(1, 1, 1 + 4 ϕ)$	$(2 + 3 ϕ, - 2, - (1 + ϕ))$	9	30966310020358744
$(1, 1, 1 + 4 ϕ)$	$(3 ϕ, - (2 + 2 ϕ), - (1 + ϕ))$	9	31273154885136896
$(1, 1, 1 + 4 ϕ)$	$(- (1 + ϕ), 2 + 3 ϕ, - 2)$	9	31427335487092792
$(1, 1, 1 + 4 ϕ)$	$(- 1, - (1 + 4 ϕ), - 1)$	9	31741135425996112
$(1, 1, 1 + 4 ϕ)$	$(- (1 + 4 ϕ), - 1, - 1)$	9	31741135425996112
$(1, 1, 1 + 4 ϕ)$	$(2 ϕ, 1 + 3 ϕ, - (1 + ϕ))$	9	31847977384066712
$(1, 1, 1 + 4 ϕ)$	$(- (1 + 2 ϕ), - (3 + 2 ϕ), - 1)$	9	31847977384066712
$(1, 1, 1 + 4 ϕ)$	$(1 + ϕ, - (2 + 3 ϕ), - 2)$	9	31862567289135024
$(1, 1, 1 + 4 ϕ)$	$(- 3 ϕ, 2 + 2 ϕ, - (1 + ϕ))$	9	31862567289135024
$(1, 1, 1 + 4 ϕ)$	$(3 + 2 ϕ, 1, - (1 + 2 ϕ))$	9	32211939458540080
$(1, 1, 1 + 4 ϕ)$	$(- (2 + 3 ϕ), 2, - (1 + ϕ))$	9	32211939458540080
$(1, 1, 1 + 4 ϕ)$	$(1 + 3 ϕ, - (1 + ϕ), - 2 ϕ)$	10	31379936441261904
$(1, 1, 1 + 4 ϕ)$	$(- (1 + 3 ϕ), 1 + ϕ, - 2 ϕ)$	10	32310291423550048
$(1, 1, 1 + 4 ϕ)$	$(3 + 2 ϕ, - 1, - (1 + 2 ϕ))$	10	32310291423550048
$(1, 1, 1 + 4 ϕ)$	$(- (1 + ϕ), - (2 + 3 ϕ), - 2)$	10	32434523158688432
$(1, 1, 1 + 4 ϕ)$	$(- 2 ϕ, 1 + 3 ϕ, - (1 + ϕ))$	10	32434523158688432
$(1, 1, 1 + 4 ϕ)$	$(2 ϕ, - (1 + 3 ϕ), - (1 + ϕ))$	10	32546264786259632
$(1, 1, 1 + 4 ϕ)$	$(- 3 ϕ, - (2 + 2 ϕ), - (1 + ϕ))$	10	32546264786259632
$(1, 1, 1 + 4 ϕ)$	$(2 + 2 ϕ, 1 + ϕ, - 3 ϕ)$	10	32554921652946288
$(1, 1, 1 + 4 ϕ)$	$(- (2 + 3 ϕ), - 2, - (1 + ϕ))$	10	32554921652946288
$(1, 1, 1 + 4 ϕ)$	$(1 + ϕ, 3 ϕ, - (2 + 2 ϕ))$	10	32784976383088008
$(1, 1, 1 + 4 ϕ)$	$(- (3 + 2 ϕ), 1, - (1 + 2 ϕ))$	10	33402081403100912
$(1, 1, 1 + 4 ϕ)$	$(2 + 2 ϕ, - (1 + ϕ), - 3 ϕ)$	11	32799828186048560
$(1, 1, 1 + 4 ϕ)$	$(- (1 + 3 ϕ), - (1 + ϕ), - 2 ϕ)$	11	32799828186048560
$(1, 1, 1 + 4 ϕ)$	$(- 2 ϕ, - (1 + 3 ϕ), - (1 + ϕ))$	11	33161367444506896
$(1, 1, 1 + 4 ϕ)$	$(- (1 + ϕ), 3 ϕ, - (2 + 2 ϕ))$	11	33192990345476336
$(1, 1, 1 + 4 ϕ)$	$(1 + ϕ, 2 ϕ, - (1 + 3 ϕ))$	11	33192990345476336
$(1, 1, 1 + 4 ϕ)$	$(1, 1 + 2 ϕ, - (3 + 2 ϕ))$	11	33352557286121456
$(1, 1, 1 + 4 ϕ)$	$(1 + ϕ, - 3 ϕ, - (2 + 2 ϕ))$	11	33352557286121456
$(1, 1, 1 + 4 ϕ)$	$(- (2 + 2 ϕ), 1 + ϕ, - 3 ϕ)$	11	33520884207303232
$(1, 1, 1 + 4 ϕ)$	$(- (3 + 2 ϕ), - 1, - (1 + 2 ϕ))$	11	33520884207303232
$(1, 1, 1 + 4 ϕ)$	$(- 1, 1 + 2 ϕ, - (3 + 2 ϕ))$	12	33498884466962288
$(1, 1, 1 + 4 ϕ)$	$(1 + ϕ, - 2 ϕ, - (1 + 3 ϕ))$	12	33498884466962288
$(1, 1, 1 + 4 ϕ)$	$(2, 1 + ϕ, - (2 + 3 ϕ))$	12	33762653736339312
$(1, 1, 1 + 4 ϕ)$	$(- (1 + ϕ), - 3 ϕ, - (2 + 2 ϕ))$	12	33762653736339312
$(1, 1, 1 + 4 ϕ)$	$(- (2 + 2 ϕ), - (1 + ϕ), - 3 ϕ)$	12	33797546306714080
$(1, 1, 1 + 4 ϕ)$	$(- (1 + ϕ), 2 ϕ, - (1 + 3 ϕ))$	12	33826889941291328
$(1, 1, 1 + 4 ϕ)$	$(1, - (1 + 2 ϕ), - (3 + 2 ϕ))$	12	33867550839819360
$(1, 1, 1 + 4 ϕ)$	$(- 1, - (1 + 2 ϕ), - (3 + 2 ϕ))$	13	34010665352864416
$(1, 1, 1 + 4 ϕ)$	$(2, - (1 + ϕ), - (2 + 3 ϕ))$	13	34010665352864416
$(1, 1, 1 + 4 ϕ)$	$(- 2, 1 + ϕ, - (2 + 3 ϕ))$	13	34138347673368800
$(1, 1, 1 + 4 ϕ)$	$(- (1 + ϕ), - 2 ϕ, - (1 + 3 ϕ))$	13	34138347673368800
$(1, 1, 1 + 4 ϕ)$	$(1, 1, - (1 + 4 ϕ))$	13	34153139412339152
$(1, 1, 1 + 4 ϕ)$	$(1, - 1, - (1 + 4 ϕ))$	14	34241968156226656
$(1, 1, 1 + 4 ϕ)$	$(- 2, - (1 + ϕ), - (2 + 3 ϕ))$	14	34374390351539520
$(1, 1, 1 + 4 ϕ)$	$(- 1, 1, - (1 + 4 ϕ))$	14	34377902116857504
$(1, 1, 1 + 4 ϕ)$	$(- 1, - 1, - (1 + 4 ϕ))$	15	34460645968551616

捻れ立方体

捻れ立方体
始点	終点	最短経路の長さ	経路の個数
$(c_{1}, c_{2}, c_{3})$	$(c_{1}, c_{2}, c_{3})$	0	1
$(c_{1}, c_{2}, c_{3})$	$(c_{2}, c_{3}, c_{1})$	1	21480681
$(c_{1}, c_{2}, c_{3})$	$(c_{3}, c_{1}, c_{2})$	1	21480681
$(c_{1}, c_{2}, c_{3})$	$(- c_{1}, c_{3}, c_{2})$	1	21485947
$(c_{1}, c_{2}, c_{3})$	$(c_{2}, - c_{1}, c_{3})$	1	22129907
$(c_{1}, c_{2}, c_{3})$	$(- c_{2}, c_{1}, c_{3})$	1	22129907
$(c_{1}, c_{2}, c_{3})$	$(- c_{1}, - c_{2}, c_{3})$	2	22488236
$(c_{1}, c_{2}, c_{3})$	$(c_{3}, c_{2}, - c_{1})$	2	24940883
$(c_{1}, c_{2}, c_{3})$	$(- c_{3}, c_{2}, c_{1})$	2	24940883
$(c_{1}, c_{2}, c_{3})$	$(c_{3}, - c_{2}, c_{1})$	2	25236745
$(c_{1}, c_{2}, c_{3})$	$(c_{1}, c_{3}, - c_{2})$	2	25816818
$(c_{1}, c_{2}, c_{3})$	$(c_{1}, - c_{3}, c_{2})$	2	25816818
$(c_{1}, c_{2}, c_{3})$	$(- c_{2}, c_{3}, - c_{1})$	2	25992134
$(c_{1}, c_{2}, c_{3})$	$(- c_{3}, - c_{1}, c_{2})$	2	25992134
$(c_{1}, c_{2}, c_{3})$	$(- c_{2}, - c_{3}, c_{1})$	3	28669633
$(c_{1}, c_{2}, c_{3})$	$(c_{3}, - c_{1}, - c_{2})$	3	28669633
$(c_{1}, c_{2}, c_{3})$	$(c_{2}, c_{1}, - c_{3})$	3	28952146
$(c_{1}, c_{2}, c_{3})$	$(- c_{1}, c_{2}, - c_{3})$	3	29193524
$(c_{1}, c_{2}, c_{3})$	$(c_{2}, - c_{3}, - c_{1})$	3	29727997
$(c_{1}, c_{2}, c_{3})$	$(- c_{3}, c_{1}, - c_{2})$	3	29727997
$(c_{1}, c_{2}, c_{3})$	$(- c_{3}, - c_{2}, - c_{1})$	3	30941406
$(c_{1}, c_{2}, c_{3})$	$(c_{1}, - c_{2}, - c_{3})$	4	31179668
$(c_{1}, c_{2}, c_{3})$	$(- c_{1}, - c_{3}, - c_{2})$	4	31611090
$(c_{1}, c_{2}, c_{3})$	$(- c_{2}, - c_{1}, - c_{3})$	4	31716277

捻れ十二面体

捻れ十二面体
始点	終点	最短経路の長さ	経路の個数
$(c_{02}, c_{03}, c_{15})$	$(c_{02}, c_{03}, c_{15})$	0	1
$(c_{02}, c_{03}, c_{15})$	$(c_{05}, - c_{04}, c_{14})$	1	4314181324075421543
$(c_{02}, c_{03}, c_{15})$	$(c_{09}, c_{01}, c_{13})$	1	4314181324075421543
$(c_{02}, c_{03}, c_{15})$	$(- c_{02}, - c_{03}, c_{15})$	1	4333711459240318005
$(c_{02}, c_{03}, c_{15})$	$(- c_{05}, c_{04}, c_{14})$	1	4522374719995599256
$(c_{02}, c_{03}, c_{15})$	$(c_{07}, c_{08}, c_{12})$	1	4522374719995599256
$(c_{02}, c_{03}, c_{15})$	$(c_{01}, c_{13}, c_{09})$	2	4650172112382110524
$(c_{02}, c_{03}, c_{15})$	$(- c_{06}, c_{10}, c_{11})$	2	4650172112382110524
$(c_{02}, c_{03}, c_{15})$	$(- c_{09}, - c_{01}, c_{13})$	2	5053289730006881156
$(c_{02}, c_{03}, c_{15})$	$(c_{11}, - c_{06}, c_{10})$	2	5053289730006881156
$(c_{02}, c_{03}, c_{15})$	$(c_{12}, c_{07}, c_{08})$	2	5117679063215239857
$(c_{02}, c_{03}, c_{15})$	$(c_{06}, - c_{10}, c_{11})$	2	5277152664987941334
$(c_{02}, c_{03}, c_{15})$	$(c_{08}, c_{12}, c_{07})$	2	5277152664987941334
$(c_{02}, c_{03}, c_{15})$	$(- c_{07}, - c_{08}, c_{12})$	2	5315282020390342573
$(c_{02}, c_{03}, c_{15})$	$(- c_{11}, c_{06}, c_{10})$	2	5315282020390342573
$(c_{02}, c_{03}, c_{15})$	$(- c_{01}, - c_{13}, c_{09})$	3	5602858379099328267
$(c_{02}, c_{03}, c_{15})$	$(- c_{04}, c_{14}, c_{05})$	3	5602858379099328267
$(c_{02}, c_{03}, c_{15})$	$(c_{10}, - c_{11}, c_{06})$	3	5959387902449397235
$(c_{02}, c_{03}, c_{15})$	$(- c_{10}, c_{11}, c_{06})$	3	5964380694857913506
$(c_{02}, c_{03}, c_{15})$	$(c_{14}, - c_{05}, c_{04})$	3	5964380694857913506
$(c_{02}, c_{03}, c_{15})$	$(c_{03}, c_{15}, c_{02})$	3	5979260073377957876
$(c_{02}, c_{03}, c_{15})$	$(c_{15}, c_{02}, c_{03})$	3	5979260073377957876
$(c_{02}, c_{03}, c_{15})$	$(c_{04}, - c_{14}, c_{05})$	3	6131997869373884282
$(c_{02}, c_{03}, c_{15})$	$(- c_{08}, - c_{12}, c_{07})$	3	6131997869373884282
$(c_{02}, c_{03}, c_{15})$	$(- c_{12}, - c_{07}, c_{08})$	3	6137589861008701982
$(c_{02}, c_{03}, c_{15})$	$(c_{13}, c_{09}, c_{01})$	3	6137589861008701982
$(c_{02}, c_{03}, c_{15})$	$(- c_{14}, c_{05}, c_{04})$	3	6462245971919901062
$(c_{02}, c_{03}, c_{15})$	$(- c_{03}, - c_{15}, c_{02})$	4	6517224986620782954
$(c_{02}, c_{03}, c_{15})$	$(c_{15}, - c_{02}, - c_{03})$	4	6517224986620782954
$(c_{02}, c_{03}, c_{15})$	$(c_{13}, - c_{09}, - c_{01})$	4	6626302580218494509
$(c_{02}, c_{03}, c_{15})$	$(c_{14}, c_{05}, - c_{04})$	4	6626302580218494509
$(c_{02}, c_{03}, c_{15})$	$(- c_{03}, c_{15}, - c_{02})$	4	6644747063769147116
$(c_{02}, c_{03}, c_{15})$	$(- c_{15}, - c_{02}, c_{03})$	4	6644747063769147116
$(c_{02}, c_{03}, c_{15})$	$(c_{10}, c_{11}, - c_{06})$	4	6755481808762443275
$(c_{02}, c_{03}, c_{15})$	$(- c_{13}, c_{09}, - c_{01})$	4	6755481808762443275
$(c_{02}, c_{03}, c_{15})$	$(c_{04}, c_{14}, - c_{05})$	4	6759306272127652530
$(c_{02}, c_{03}, c_{15})$	$(- c_{13}, - c_{09}, c_{01})$	4	6759916916383372014
$(c_{02}, c_{03}, c_{15})$	$(c_{03}, - c_{15}, - c_{02})$	4	6908157265078338965
$(c_{02}, c_{03}, c_{15})$	$(- c_{15}, c_{02}, - c_{03})$	4	6908157265078338965
$(c_{02}, c_{03}, c_{15})$	$(- c_{08}, c_{12}, - c_{07})$	5	6914484419509852736
$(c_{02}, c_{03}, c_{15})$	$(- c_{01}, c_{13}, - c_{09})$	5	7042082338055373837
$(c_{02}, c_{03}, c_{15})$	$(c_{08}, - c_{12}, - c_{07})$	5	7042082338055373837
$(c_{02}, c_{03}, c_{15})$	$(c_{12}, - c_{07}, - c_{08})$	5	7060702075089394041
$(c_{02}, c_{03}, c_{15})$	$(- c_{14}, - c_{05}, - c_{04})$	5	7060702075089394041
$(c_{02}, c_{03}, c_{15})$	$(- c_{04}, - c_{14}, - c_{05})$	5	7095332315629856884
$(c_{02}, c_{03}, c_{15})$	$(c_{06}, c_{10}, - c_{11})$	5	7095332315629856884
$(c_{02}, c_{03}, c_{15})$	$(c_{11}, c_{06}, - c_{10})$	5	7109104848582737640
$(c_{02}, c_{03}, c_{15})$	$(- c_{10}, - c_{11}, - c_{06})$	5	7129904253032921109
$(c_{02}, c_{03}, c_{15})$	$(- c_{12}, c_{07}, - c_{08})$	5	7129904253032921109
$(c_{02}, c_{03}, c_{15})$	$(c_{01}, - c_{13}, - c_{09})$	5	7243443668446620541
$(c_{02}, c_{03}, c_{15})$	$(- c_{07}, c_{08}, - c_{12})$	6	7291027247966187042
$(c_{02}, c_{03}, c_{15})$	$(c_{09}, - c_{01}, - c_{13})$	6	7291027247966187042
$(c_{02}, c_{03}, c_{15})$	$(c_{07}, - c_{08}, - c_{12})$	6	7321713647578339820
$(c_{02}, c_{03}, c_{15})$	$(- c_{06}, - c_{10}, - c_{11})$	6	7350875787612380280
$(c_{02}, c_{03}, c_{15})$	$(c_{05}, c_{04}, - c_{14})$	6	7358921524534296466
$(c_{02}, c_{03}, c_{15})$	$(- c_{11}, - c_{06}, - c_{10})$	6	7358921524534296466
$(c_{02}, c_{03}, c_{15})$	$(- c_{09}, c_{01}, - c_{13})$	6	7422833893678375536
$(c_{02}, c_{03}, c_{15})$	$(c_{02}, - c_{03}, - c_{15})$	7	7466859697456930963
$(c_{02}, c_{03}, c_{15})$	$(- c_{02}, c_{03}, - c_{15})$	7	7473130927173084026
$(c_{02}, c_{03}, c_{15})$	$(- c_{05}, - c_{04}, - c_{14})$	7	7494435457496789482