Polytope of Type {2,12,4,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,4,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,157550)
Rank : 5
Schlafli Type : {2,12,4,3}
Number of vertices, edges, etc : 2, 12, 48, 12, 6
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 : {2,6,4,3}*576
3-fold quotients : {2,4,4,3}*384b
4-fold quotients : {2,12,2,3}*288
6-fold quotients : {2,2,4,3}*192
8-fold quotients : {2,6,2,3}*144
12-fold quotients : {2,4,2,3}*96, {2,2,4,3}*96
16-fold quotients : {2,3,2,3}*72
24-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 7, 11)( 8, 12)( 9, 13)( 10, 14)( 19, 23)( 20, 24)( 21, 25)( 22, 26)
( 31, 35)( 32, 36)( 33, 37)( 34, 38)( 43, 47)( 44, 48)( 45, 49)( 46, 50)
( 55, 59)( 56, 60)( 57, 61)( 58, 62)( 67, 71)( 68, 72)( 69, 73)( 70, 74)
( 75,111)( 76,112)( 77,113)( 78,114)( 79,119)( 80,120)( 81,121)( 82,122)
( 83,115)( 84,116)( 85,117)( 86,118)( 87,123)( 88,124)( 89,125)( 90,126)
( 91,131)( 92,132)( 93,133)( 94,134)( 95,127)( 96,128)( 97,129)( 98,130)
( 99,135)(100,136)(101,137)(102,138)(103,143)(104,144)(105,145)(106,146)
(107,139)(108,140)(109,141)(110,142);;
s2 := ( 3, 81)( 4, 82)( 5, 79)( 6, 80)( 7, 77)( 8, 78)( 9, 75)( 10, 76)
( 11, 85)( 12, 86)( 13, 83)( 14, 84)( 15, 93)( 16, 94)( 17, 91)( 18, 92)
( 19, 89)( 20, 90)( 21, 87)( 22, 88)( 23, 97)( 24, 98)( 25, 95)( 26, 96)
( 27,105)( 28,106)( 29,103)( 30,104)( 31,101)( 32,102)( 33, 99)( 34,100)
( 35,109)( 36,110)( 37,107)( 38,108)( 39,117)( 40,118)( 41,115)( 42,116)
( 43,113)( 44,114)( 45,111)( 46,112)( 47,121)( 48,122)( 49,119)( 50,120)
( 51,129)( 52,130)( 53,127)( 54,128)( 55,125)( 56,126)( 57,123)( 58,124)
( 59,133)( 60,134)( 61,131)( 62,132)( 63,141)( 64,142)( 65,139)( 66,140)
( 67,137)( 68,138)( 69,135)( 70,136)( 71,145)( 72,146)( 73,143)( 74,144);;
s3 := ( 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);;
s4 := ( 3, 27)( 4, 30)( 5, 29)( 6, 28)( 7, 31)( 8, 34)( 9, 33)( 10, 32)
( 11, 35)( 12, 38)( 13, 37)( 14, 36)( 16, 18)( 20, 22)( 24, 26)( 39, 63)
( 40, 66)( 41, 65)( 42, 64)( 43, 67)( 44, 70)( 45, 69)( 46, 68)( 47, 71)
( 48, 74)( 49, 73)( 50, 72)( 52, 54)( 56, 58)( 60, 62)( 75, 99)( 76,102)
( 77,101)( 78,100)( 79,103)( 80,106)( 81,105)( 82,104)( 83,107)( 84,110)
( 85,109)( 86,108)( 88, 90)( 92, 94)( 96, 98)(111,135)(112,138)(113,137)
(114,136)(115,139)(116,142)(117,141)(118,140)(119,143)(120,146)(121,145)
(122,144)(124,126)(128,130)(132,134);;
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,
s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, 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)!( 7, 11)( 8, 12)( 9, 13)( 10, 14)( 19, 23)( 20, 24)( 21, 25)
( 22, 26)( 31, 35)( 32, 36)( 33, 37)( 34, 38)( 43, 47)( 44, 48)( 45, 49)
( 46, 50)( 55, 59)( 56, 60)( 57, 61)( 58, 62)( 67, 71)( 68, 72)( 69, 73)
( 70, 74)( 75,111)( 76,112)( 77,113)( 78,114)( 79,119)( 80,120)( 81,121)
( 82,122)( 83,115)( 84,116)( 85,117)( 86,118)( 87,123)( 88,124)( 89,125)
( 90,126)( 91,131)( 92,132)( 93,133)( 94,134)( 95,127)( 96,128)( 97,129)
( 98,130)( 99,135)(100,136)(101,137)(102,138)(103,143)(104,144)(105,145)
(106,146)(107,139)(108,140)(109,141)(110,142);
s2 := Sym(146)!( 3, 81)( 4, 82)( 5, 79)( 6, 80)( 7, 77)( 8, 78)( 9, 75)
( 10, 76)( 11, 85)( 12, 86)( 13, 83)( 14, 84)( 15, 93)( 16, 94)( 17, 91)
( 18, 92)( 19, 89)( 20, 90)( 21, 87)( 22, 88)( 23, 97)( 24, 98)( 25, 95)
( 26, 96)( 27,105)( 28,106)( 29,103)( 30,104)( 31,101)( 32,102)( 33, 99)
( 34,100)( 35,109)( 36,110)( 37,107)( 38,108)( 39,117)( 40,118)( 41,115)
( 42,116)( 43,113)( 44,114)( 45,111)( 46,112)( 47,121)( 48,122)( 49,119)
( 50,120)( 51,129)( 52,130)( 53,127)( 54,128)( 55,125)( 56,126)( 57,123)
( 58,124)( 59,133)( 60,134)( 61,131)( 62,132)( 63,141)( 64,142)( 65,139)
( 66,140)( 67,137)( 68,138)( 69,135)( 70,136)( 71,145)( 72,146)( 73,143)
( 74,144);
s3 := 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);
s4 := Sym(146)!( 3, 27)( 4, 30)( 5, 29)( 6, 28)( 7, 31)( 8, 34)( 9, 33)
( 10, 32)( 11, 35)( 12, 38)( 13, 37)( 14, 36)( 16, 18)( 20, 22)( 24, 26)
( 39, 63)( 40, 66)( 41, 65)( 42, 64)( 43, 67)( 44, 70)( 45, 69)( 46, 68)
( 47, 71)( 48, 74)( 49, 73)( 50, 72)( 52, 54)( 56, 58)( 60, 62)( 75, 99)
( 76,102)( 77,101)( 78,100)( 79,103)( 80,106)( 81,105)( 82,104)( 83,107)
( 84,110)( 85,109)( 86,108)( 88, 90)( 92, 94)( 96, 98)(111,135)(112,138)
(113,137)(114,136)(115,139)(116,142)(117,141)(118,140)(119,143)(120,146)
(121,145)(122,144)(124,126)(128,130)(132,134);
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, s3*s4*s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
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