Polytope of Type {2,4,6,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,12}*1152c
if this polytope has a name.
Group : SmallGroup(1152,136351)
Rank : 5
Schlafli Type : {2,4,6,12}
Number of vertices, edges, etc : 2, 4, 12, 36, 12
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 : {2,2,6,12}*576b, {2,4,6,6}*576c
3-fold quotients : {2,4,2,12}*384
4-fold quotients : {2,4,6,3}*288, {2,2,6,6}*288b
6-fold quotients : {2,2,2,12}*192, {2,4,2,6}*192
8-fold quotients : {2,2,6,3}*144
9-fold quotients : {2,4,2,4}*128
12-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96
18-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
24-fold quotients : {2,2,2,3}*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 := ( 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);;
s2 := ( 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);;
s3 := ( 3, 4)( 6, 10)( 7, 9)( 8, 11)( 12, 13)( 15, 19)( 16, 18)( 17, 20)
( 21, 22)( 24, 28)( 25, 27)( 26, 29)( 30, 31)( 33, 37)( 34, 36)( 35, 38)
( 39, 58)( 40, 57)( 41, 59)( 42, 64)( 43, 63)( 44, 65)( 45, 61)( 46, 60)
( 47, 62)( 48, 67)( 49, 66)( 50, 68)( 51, 73)( 52, 72)( 53, 74)( 54, 70)
( 55, 69)( 56, 71)( 75, 76)( 78, 82)( 79, 81)( 80, 83)( 84, 85)( 87, 91)
( 88, 90)( 89, 92)( 93, 94)( 96,100)( 97, 99)( 98,101)(102,103)(105,109)
(106,108)(107,110)(111,130)(112,129)(113,131)(114,136)(115,135)(116,137)
(117,133)(118,132)(119,134)(120,139)(121,138)(122,140)(123,145)(124,144)
(125,146)(126,142)(127,141)(128,143);;
s4 := ( 3, 42)( 4, 44)( 5, 43)( 6, 39)( 7, 41)( 8, 40)( 9, 45)( 10, 47)
( 11, 46)( 12, 51)( 13, 53)( 14, 52)( 15, 48)( 16, 50)( 17, 49)( 18, 54)
( 19, 56)( 20, 55)( 21, 60)( 22, 62)( 23, 61)( 24, 57)( 25, 59)( 26, 58)
( 27, 63)( 28, 65)( 29, 64)( 30, 69)( 31, 71)( 32, 70)( 33, 66)( 34, 68)
( 35, 67)( 36, 72)( 37, 74)( 38, 73)( 75,114)( 76,116)( 77,115)( 78,111)
( 79,113)( 80,112)( 81,117)( 82,119)( 83,118)( 84,123)( 85,125)( 86,124)
( 87,120)( 88,122)( 89,121)( 90,126)( 91,128)( 92,127)( 93,132)( 94,134)
( 95,133)( 96,129)( 97,131)( 98,130)( 99,135)(100,137)(101,136)(102,141)
(103,143)(104,142)(105,138)(106,140)(107,139)(108,144)(109,146)(110,145);;
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := 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);
s2 := 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);
s3 := Sym(146)!( 3, 4)( 6, 10)( 7, 9)( 8, 11)( 12, 13)( 15, 19)( 16, 18)
( 17, 20)( 21, 22)( 24, 28)( 25, 27)( 26, 29)( 30, 31)( 33, 37)( 34, 36)
( 35, 38)( 39, 58)( 40, 57)( 41, 59)( 42, 64)( 43, 63)( 44, 65)( 45, 61)
( 46, 60)( 47, 62)( 48, 67)( 49, 66)( 50, 68)( 51, 73)( 52, 72)( 53, 74)
( 54, 70)( 55, 69)( 56, 71)( 75, 76)( 78, 82)( 79, 81)( 80, 83)( 84, 85)
( 87, 91)( 88, 90)( 89, 92)( 93, 94)( 96,100)( 97, 99)( 98,101)(102,103)
(105,109)(106,108)(107,110)(111,130)(112,129)(113,131)(114,136)(115,135)
(116,137)(117,133)(118,132)(119,134)(120,139)(121,138)(122,140)(123,145)
(124,144)(125,146)(126,142)(127,141)(128,143);
s4 := Sym(146)!( 3, 42)( 4, 44)( 5, 43)( 6, 39)( 7, 41)( 8, 40)( 9, 45)
( 10, 47)( 11, 46)( 12, 51)( 13, 53)( 14, 52)( 15, 48)( 16, 50)( 17, 49)
( 18, 54)( 19, 56)( 20, 55)( 21, 60)( 22, 62)( 23, 61)( 24, 57)( 25, 59)
( 26, 58)( 27, 63)( 28, 65)( 29, 64)( 30, 69)( 31, 71)( 32, 70)( 33, 66)
( 34, 68)( 35, 67)( 36, 72)( 37, 74)( 38, 73)( 75,114)( 76,116)( 77,115)
( 78,111)( 79,113)( 80,112)( 81,117)( 82,119)( 83,118)( 84,123)( 85,125)
( 86,124)( 87,120)( 88,122)( 89,121)( 90,126)( 91,128)( 92,127)( 93,132)
( 94,134)( 95,133)( 96,129)( 97,131)( 98,130)( 99,135)(100,137)(101,136)
(102,141)(103,143)(104,142)(105,138)(106,140)(107,139)(108,144)(109,146)
(110,145);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope