Polytope of Type {2,12,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6,4}*1152c
if this polytope has a name.
Group : SmallGroup(1152,136351)
Rank : 5
Schlafli Type : {2,12,6,4}
Number of vertices, edges, etc : 2, 12, 36, 12, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,12,6,2}*576b, {2,6,6,4}*576c
3-fold quotients : {2,12,2,4}*384
4-fold quotients : {2,3,6,4}*288, {2,6,6,2}*288c
6-fold quotients : {2,12,2,2}*192, {2,6,2,4}*192
8-fold quotients : {2,3,6,2}*144
9-fold quotients : {2,4,2,4}*128
12-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
18-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
24-fold quotients : {2,3,2,2}*48
36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)
( 22, 23)( 24, 27)( 25, 29)( 26, 28)( 31, 32)( 33, 36)( 34, 38)( 35, 37)
( 39, 57)( 40, 59)( 41, 58)( 42, 63)( 43, 65)( 44, 64)( 45, 60)( 46, 62)
( 47, 61)( 48, 66)( 49, 68)( 50, 67)( 51, 72)( 52, 74)( 53, 73)( 54, 69)
( 55, 71)( 56, 70)( 76, 77)( 78, 81)( 79, 83)( 80, 82)( 85, 86)( 87, 90)
( 88, 92)( 89, 91)( 94, 95)( 96, 99)( 97,101)( 98,100)(103,104)(105,108)
(106,110)(107,109)(111,129)(112,131)(113,130)(114,135)(115,137)(116,136)
(117,132)(118,134)(119,133)(120,138)(121,140)(122,139)(123,144)(124,146)
(125,145)(126,141)(127,143)(128,142);;
s2 := ( 3, 43)( 4, 42)( 5, 44)( 6, 40)( 7, 39)( 8, 41)( 9, 46)( 10, 45)
( 11, 47)( 12, 52)( 13, 51)( 14, 53)( 15, 49)( 16, 48)( 17, 50)( 18, 55)
( 19, 54)( 20, 56)( 21, 61)( 22, 60)( 23, 62)( 24, 58)( 25, 57)( 26, 59)
( 27, 64)( 28, 63)( 29, 65)( 30, 70)( 31, 69)( 32, 71)( 33, 67)( 34, 66)
( 35, 68)( 36, 73)( 37, 72)( 38, 74)( 75,115)( 76,114)( 77,116)( 78,112)
( 79,111)( 80,113)( 81,118)( 82,117)( 83,119)( 84,124)( 85,123)( 86,125)
( 87,121)( 88,120)( 89,122)( 90,127)( 91,126)( 92,128)( 93,133)( 94,132)
( 95,134)( 96,130)( 97,129)( 98,131)( 99,136)(100,135)(101,137)(102,142)
(103,141)(104,143)(105,139)(106,138)(107,140)(108,145)(109,144)(110,146);;
s3 := ( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)( 49, 50)
( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)( 73, 74)
( 75, 84)( 76, 86)( 77, 85)( 78, 87)( 79, 89)( 80, 88)( 81, 90)( 82, 92)
( 83, 91)( 93,102)( 94,104)( 95,103)( 96,105)( 97,107)( 98,106)( 99,108)
(100,110)(101,109)(111,120)(112,122)(113,121)(114,123)(115,125)(116,124)
(117,126)(118,128)(119,127)(129,138)(130,140)(131,139)(132,141)(133,143)
(134,142)(135,144)(136,146)(137,145);;
s4 := ( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)( 9, 81)( 10, 82)
( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)( 18, 90)
( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)( 25, 97)( 26, 98)
( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)( 33,105)( 34,106)
( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)( 41,113)( 42,114)
( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)( 49,121)( 50,122)
( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)( 57,129)( 58,130)
( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)( 65,137)( 66,138)
( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)( 73,145)( 74,146);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)
( 17, 19)( 22, 23)( 24, 27)( 25, 29)( 26, 28)( 31, 32)( 33, 36)( 34, 38)
( 35, 37)( 39, 57)( 40, 59)( 41, 58)( 42, 63)( 43, 65)( 44, 64)( 45, 60)
( 46, 62)( 47, 61)( 48, 66)( 49, 68)( 50, 67)( 51, 72)( 52, 74)( 53, 73)
( 54, 69)( 55, 71)( 56, 70)( 76, 77)( 78, 81)( 79, 83)( 80, 82)( 85, 86)
( 87, 90)( 88, 92)( 89, 91)( 94, 95)( 96, 99)( 97,101)( 98,100)(103,104)
(105,108)(106,110)(107,109)(111,129)(112,131)(113,130)(114,135)(115,137)
(116,136)(117,132)(118,134)(119,133)(120,138)(121,140)(122,139)(123,144)
(124,146)(125,145)(126,141)(127,143)(128,142);
s2 := Sym(146)!( 3, 43)( 4, 42)( 5, 44)( 6, 40)( 7, 39)( 8, 41)( 9, 46)
( 10, 45)( 11, 47)( 12, 52)( 13, 51)( 14, 53)( 15, 49)( 16, 48)( 17, 50)
( 18, 55)( 19, 54)( 20, 56)( 21, 61)( 22, 60)( 23, 62)( 24, 58)( 25, 57)
( 26, 59)( 27, 64)( 28, 63)( 29, 65)( 30, 70)( 31, 69)( 32, 71)( 33, 67)
( 34, 66)( 35, 68)( 36, 73)( 37, 72)( 38, 74)( 75,115)( 76,114)( 77,116)
( 78,112)( 79,111)( 80,113)( 81,118)( 82,117)( 83,119)( 84,124)( 85,123)
( 86,125)( 87,121)( 88,120)( 89,122)( 90,127)( 91,126)( 92,128)( 93,133)
( 94,132)( 95,134)( 96,130)( 97,129)( 98,131)( 99,136)(100,135)(101,137)
(102,142)(103,141)(104,143)(105,139)(106,138)(107,140)(108,145)(109,144)
(110,146);
s3 := Sym(146)!( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)
( 49, 50)( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)
( 73, 74)( 75, 84)( 76, 86)( 77, 85)( 78, 87)( 79, 89)( 80, 88)( 81, 90)
( 82, 92)( 83, 91)( 93,102)( 94,104)( 95,103)( 96,105)( 97,107)( 98,106)
( 99,108)(100,110)(101,109)(111,120)(112,122)(113,121)(114,123)(115,125)
(116,124)(117,126)(118,128)(119,127)(129,138)(130,140)(131,139)(132,141)
(133,143)(134,142)(135,144)(136,146)(137,145);
s4 := Sym(146)!( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)( 9, 81)
( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)
( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)( 25, 97)
( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)( 33,105)
( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)( 41,113)
( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)( 49,121)
( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)( 57,129)
( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)( 65,137)
( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)( 73,145)
( 74,146);
poly := sub<Sym(146)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope