Polytope of Type {2,3,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,157640)
Rank : 5
Schlafli Type : {2,3,6,4}
Number of vertices, edges, etc : 2, 12, 36, 48, 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 : {2,3,6,2}*576
3-fold quotients : {2,3,6,4}*384
4-fold quotients : {2,3,6,4}*288
6-fold quotients : {2,3,6,2}*192
8-fold quotients : {2,3,6,2}*144
12-fold quotients : {2,3,2,4}*96, {2,3,3,2}*96
24-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 15, 27)( 16, 29)( 17, 28)
( 18, 30)( 19, 35)( 20, 37)( 21, 36)( 22, 38)( 23, 31)( 24, 33)( 25, 32)
( 26, 34)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 51, 63)( 52, 65)
( 53, 64)( 54, 66)( 55, 71)( 56, 73)( 57, 72)( 58, 74)( 59, 67)( 60, 69)
( 61, 68)( 62, 70)( 76, 77)( 79, 83)( 80, 85)( 81, 84)( 82, 86)( 87, 99)
( 88,101)( 89,100)( 90,102)( 91,107)( 92,109)( 93,108)( 94,110)( 95,103)
( 96,105)( 97,104)( 98,106)(112,113)(115,119)(116,121)(117,120)(118,122)
(123,135)(124,137)(125,136)(126,138)(127,143)(128,145)(129,144)(130,146)
(131,139)(132,141)(133,140)(134,142);;
s2 := ( 3, 19)( 4, 20)( 5, 22)( 6, 21)( 7, 15)( 8, 16)( 9, 18)( 10, 17)
( 11, 23)( 12, 24)( 13, 26)( 14, 25)( 27, 31)( 28, 32)( 29, 34)( 30, 33)
( 37, 38)( 39, 55)( 40, 56)( 41, 58)( 42, 57)( 43, 51)( 44, 52)( 45, 54)
( 46, 53)( 47, 59)( 48, 60)( 49, 62)( 50, 61)( 63, 67)( 64, 68)( 65, 70)
( 66, 69)( 73, 74)( 75, 91)( 76, 92)( 77, 94)( 78, 93)( 79, 87)( 80, 88)
( 81, 90)( 82, 89)( 83, 95)( 84, 96)( 85, 98)( 86, 97)( 99,103)(100,104)
(101,106)(102,105)(109,110)(111,127)(112,128)(113,130)(114,129)(115,123)
(116,124)(117,126)(118,125)(119,131)(120,132)(121,134)(122,133)(135,139)
(136,140)(137,142)(138,141)(145,146);;
s3 := ( 3, 6)( 7, 10)( 11, 14)( 15, 30)( 16, 28)( 17, 29)( 18, 27)( 19, 34)
( 20, 32)( 21, 33)( 22, 31)( 23, 38)( 24, 36)( 25, 37)( 26, 35)( 39, 42)
( 43, 46)( 47, 50)( 51, 66)( 52, 64)( 53, 65)( 54, 63)( 55, 70)( 56, 68)
( 57, 69)( 58, 67)( 59, 74)( 60, 72)( 61, 73)( 62, 71)( 75,114)( 76,112)
( 77,113)( 78,111)( 79,118)( 80,116)( 81,117)( 82,115)( 83,122)( 84,120)
( 85,121)( 86,119)( 87,138)( 88,136)( 89,137)( 90,135)( 91,142)( 92,140)
( 93,141)( 94,139)( 95,146)( 96,144)( 97,145)( 98,143)( 99,126)(100,124)
(101,125)(102,123)(103,130)(104,128)(105,129)(106,127)(107,134)(108,132)
(109,133)(110,131);;
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,
s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 15, 27)( 16, 29)
( 17, 28)( 18, 30)( 19, 35)( 20, 37)( 21, 36)( 22, 38)( 23, 31)( 24, 33)
( 25, 32)( 26, 34)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 51, 63)
( 52, 65)( 53, 64)( 54, 66)( 55, 71)( 56, 73)( 57, 72)( 58, 74)( 59, 67)
( 60, 69)( 61, 68)( 62, 70)( 76, 77)( 79, 83)( 80, 85)( 81, 84)( 82, 86)
( 87, 99)( 88,101)( 89,100)( 90,102)( 91,107)( 92,109)( 93,108)( 94,110)
( 95,103)( 96,105)( 97,104)( 98,106)(112,113)(115,119)(116,121)(117,120)
(118,122)(123,135)(124,137)(125,136)(126,138)(127,143)(128,145)(129,144)
(130,146)(131,139)(132,141)(133,140)(134,142);
s2 := Sym(146)!( 3, 19)( 4, 20)( 5, 22)( 6, 21)( 7, 15)( 8, 16)( 9, 18)
( 10, 17)( 11, 23)( 12, 24)( 13, 26)( 14, 25)( 27, 31)( 28, 32)( 29, 34)
( 30, 33)( 37, 38)( 39, 55)( 40, 56)( 41, 58)( 42, 57)( 43, 51)( 44, 52)
( 45, 54)( 46, 53)( 47, 59)( 48, 60)( 49, 62)( 50, 61)( 63, 67)( 64, 68)
( 65, 70)( 66, 69)( 73, 74)( 75, 91)( 76, 92)( 77, 94)( 78, 93)( 79, 87)
( 80, 88)( 81, 90)( 82, 89)( 83, 95)( 84, 96)( 85, 98)( 86, 97)( 99,103)
(100,104)(101,106)(102,105)(109,110)(111,127)(112,128)(113,130)(114,129)
(115,123)(116,124)(117,126)(118,125)(119,131)(120,132)(121,134)(122,133)
(135,139)(136,140)(137,142)(138,141)(145,146);
s3 := Sym(146)!( 3, 6)( 7, 10)( 11, 14)( 15, 30)( 16, 28)( 17, 29)( 18, 27)
( 19, 34)( 20, 32)( 21, 33)( 22, 31)( 23, 38)( 24, 36)( 25, 37)( 26, 35)
( 39, 42)( 43, 46)( 47, 50)( 51, 66)( 52, 64)( 53, 65)( 54, 63)( 55, 70)
( 56, 68)( 57, 69)( 58, 67)( 59, 74)( 60, 72)( 61, 73)( 62, 71)( 75,114)
( 76,112)( 77,113)( 78,111)( 79,118)( 80,116)( 81,117)( 82,115)( 83,122)
( 84,120)( 85,121)( 86,119)( 87,138)( 88,136)( 89,137)( 90,135)( 91,142)
( 92,140)( 93,141)( 94,139)( 95,146)( 96,144)( 97,145)( 98,143)( 99,126)
(100,124)(101,125)(102,123)(103,130)(104,128)(105,129)(106,127)(107,134)
(108,132)(109,133)(110,131);
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, s1*s2*s1*s2*s1*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >;
to this polytope