Polytope of Type {2,3,4,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,4,12}*1152
if this polytope has a name.
Group : SmallGroup(1152,157550)
Rank : 5
Schlafli Type : {2,3,4,12}
Number of vertices, edges, etc : 2, 6, 12, 48, 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 : {2,3,4,6}*576
3-fold quotients : {2,3,4,4}*384b
4-fold quotients : {2,3,2,12}*288
6-fold quotients : {2,3,4,2}*192
8-fold quotients : {2,3,2,6}*144
12-fold quotients : {2,3,2,4}*96, {2,3,4,2}*96
16-fold quotients : {2,3,2,3}*72
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)( 8, 9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)( 19, 31)
( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)( 40, 41)
( 44, 45)( 48, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 67)( 56, 69)
( 57, 68)( 58, 70)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 76, 77)( 80, 81)
( 84, 85)( 87, 99)( 88,101)( 89,100)( 90,102)( 91,103)( 92,105)( 93,104)
( 94,106)( 95,107)( 96,109)( 97,108)( 98,110)(112,113)(116,117)(120,121)
(123,135)(124,137)(125,136)(126,138)(127,139)(128,141)(129,140)(130,142)
(131,143)(132,145)(133,144)(134,146);;
s2 := ( 3, 15)( 4, 16)( 5, 18)( 6, 17)( 7, 19)( 8, 20)( 9, 22)( 10, 21)
( 11, 23)( 12, 24)( 13, 26)( 14, 25)( 29, 30)( 33, 34)( 37, 38)( 39, 51)
( 40, 52)( 41, 54)( 42, 53)( 43, 55)( 44, 56)( 45, 58)( 46, 57)( 47, 59)
( 48, 60)( 49, 62)( 50, 61)( 65, 66)( 69, 70)( 73, 74)( 75, 87)( 76, 88)
( 77, 90)( 78, 89)( 79, 91)( 80, 92)( 81, 94)( 82, 93)( 83, 95)( 84, 96)
( 85, 98)( 86, 97)(101,102)(105,106)(109,110)(111,123)(112,124)(113,126)
(114,125)(115,127)(116,128)(117,130)(118,129)(119,131)(120,132)(121,134)
(122,133)(137,138)(141,142)(145,146);;
s3 := ( 3, 6)( 4, 5)( 7, 14)( 8, 13)( 9, 12)( 10, 11)( 15, 18)( 16, 17)
( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 27, 30)( 28, 29)( 31, 38)( 32, 37)
( 33, 36)( 34, 35)( 39, 42)( 40, 41)( 43, 50)( 44, 49)( 45, 48)( 46, 47)
( 51, 54)( 52, 53)( 55, 62)( 56, 61)( 57, 60)( 58, 59)( 63, 66)( 64, 65)
( 67, 74)( 68, 73)( 69, 72)( 70, 71)( 75,114)( 76,113)( 77,112)( 78,111)
( 79,122)( 80,121)( 81,120)( 82,119)( 83,118)( 84,117)( 85,116)( 86,115)
( 87,126)( 88,125)( 89,124)( 90,123)( 91,134)( 92,133)( 93,132)( 94,131)
( 95,130)( 96,129)( 97,128)( 98,127)( 99,138)(100,137)(101,136)(102,135)
(103,146)(104,145)(105,144)(106,143)(107,142)(108,141)(109,140)(110,139);;
s4 := ( 3, 79)( 4, 80)( 5, 81)( 6, 82)( 7, 75)( 8, 76)( 9, 77)( 10, 78)
( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 91)( 16, 92)( 17, 93)( 18, 94)
( 19, 87)( 20, 88)( 21, 89)( 22, 90)( 23, 95)( 24, 96)( 25, 97)( 26, 98)
( 27,103)( 28,104)( 29,105)( 30,106)( 31, 99)( 32,100)( 33,101)( 34,102)
( 35,107)( 36,108)( 37,109)( 38,110)( 39,115)( 40,116)( 41,117)( 42,118)
( 43,111)( 44,112)( 45,113)( 46,114)( 47,119)( 48,120)( 49,121)( 50,122)
( 51,127)( 52,128)( 53,129)( 54,130)( 55,123)( 56,124)( 57,125)( 58,126)
( 59,131)( 60,132)( 61,133)( 62,134)( 63,139)( 64,140)( 65,141)( 66,142)
( 67,135)( 68,136)( 69,137)( 70,138)( 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*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*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)!( 4, 5)( 8, 9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)
( 19, 31)( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)
( 40, 41)( 44, 45)( 48, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 67)
( 56, 69)( 57, 68)( 58, 70)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 76, 77)
( 80, 81)( 84, 85)( 87, 99)( 88,101)( 89,100)( 90,102)( 91,103)( 92,105)
( 93,104)( 94,106)( 95,107)( 96,109)( 97,108)( 98,110)(112,113)(116,117)
(120,121)(123,135)(124,137)(125,136)(126,138)(127,139)(128,141)(129,140)
(130,142)(131,143)(132,145)(133,144)(134,146);
s2 := Sym(146)!( 3, 15)( 4, 16)( 5, 18)( 6, 17)( 7, 19)( 8, 20)( 9, 22)
( 10, 21)( 11, 23)( 12, 24)( 13, 26)( 14, 25)( 29, 30)( 33, 34)( 37, 38)
( 39, 51)( 40, 52)( 41, 54)( 42, 53)( 43, 55)( 44, 56)( 45, 58)( 46, 57)
( 47, 59)( 48, 60)( 49, 62)( 50, 61)( 65, 66)( 69, 70)( 73, 74)( 75, 87)
( 76, 88)( 77, 90)( 78, 89)( 79, 91)( 80, 92)( 81, 94)( 82, 93)( 83, 95)
( 84, 96)( 85, 98)( 86, 97)(101,102)(105,106)(109,110)(111,123)(112,124)
(113,126)(114,125)(115,127)(116,128)(117,130)(118,129)(119,131)(120,132)
(121,134)(122,133)(137,138)(141,142)(145,146);
s3 := Sym(146)!( 3, 6)( 4, 5)( 7, 14)( 8, 13)( 9, 12)( 10, 11)( 15, 18)
( 16, 17)( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 27, 30)( 28, 29)( 31, 38)
( 32, 37)( 33, 36)( 34, 35)( 39, 42)( 40, 41)( 43, 50)( 44, 49)( 45, 48)
( 46, 47)( 51, 54)( 52, 53)( 55, 62)( 56, 61)( 57, 60)( 58, 59)( 63, 66)
( 64, 65)( 67, 74)( 68, 73)( 69, 72)( 70, 71)( 75,114)( 76,113)( 77,112)
( 78,111)( 79,122)( 80,121)( 81,120)( 82,119)( 83,118)( 84,117)( 85,116)
( 86,115)( 87,126)( 88,125)( 89,124)( 90,123)( 91,134)( 92,133)( 93,132)
( 94,131)( 95,130)( 96,129)( 97,128)( 98,127)( 99,138)(100,137)(101,136)
(102,135)(103,146)(104,145)(105,144)(106,143)(107,142)(108,141)(109,140)
(110,139);
s4 := Sym(146)!( 3, 79)( 4, 80)( 5, 81)( 6, 82)( 7, 75)( 8, 76)( 9, 77)
( 10, 78)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 91)( 16, 92)( 17, 93)
( 18, 94)( 19, 87)( 20, 88)( 21, 89)( 22, 90)( 23, 95)( 24, 96)( 25, 97)
( 26, 98)( 27,103)( 28,104)( 29,105)( 30,106)( 31, 99)( 32,100)( 33,101)
( 34,102)( 35,107)( 36,108)( 37,109)( 38,110)( 39,115)( 40,116)( 41,117)
( 42,118)( 43,111)( 44,112)( 45,113)( 46,114)( 47,119)( 48,120)( 49,121)
( 50,122)( 51,127)( 52,128)( 53,129)( 54,130)( 55,123)( 56,124)( 57,125)
( 58,126)( 59,131)( 60,132)( 61,133)( 62,134)( 63,139)( 64,140)( 65,141)
( 66,142)( 67,135)( 68,136)( 69,137)( 70,138)( 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*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*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