Polytope of Type {2,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6}*1152a
if this polytope has a name.
Group : SmallGroup(1152,157550)
Rank : 4
Schlafli Type : {2,12,6}
Number of vertices, edges, etc : 2, 48, 144, 24
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,6,6}*576b
   3-fold quotients : {2,12,6}*384a
   4-fold quotients : {2,12,6}*288b, {2,3,6}*288
   6-fold quotients : {2,6,6}*192
   8-fold quotients : {2,6,6}*144c
   12-fold quotients : {2,12,2}*96, {2,3,6}*96, {2,6,3}*96
   16-fold quotients : {2,3,6}*72
   24-fold quotients : {2,3,3}*48, {2,6,2}*48
   36-fold quotients : {2,4,2}*32
   48-fold quotients : {2,3,2}*24
   72-fold quotients : {2,2,2}*16
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)( 75,111)( 76,113)( 77,112)( 78,114)( 79,119)( 80,121)
( 81,120)( 82,122)( 83,115)( 84,117)( 85,116)( 86,118)( 87,135)( 88,137)
( 89,136)( 90,138)( 91,143)( 92,145)( 93,144)( 94,146)( 95,139)( 96,141)
( 97,140)( 98,142)( 99,123)(100,125)(101,124)(102,126)(103,131)(104,133)
(105,132)(106,134)(107,127)(108,129)(109,128)(110,130);;
s2 := (  3, 91)(  4, 92)(  5, 94)(  6, 93)(  7, 87)(  8, 88)(  9, 90)( 10, 89)
( 11, 95)( 12, 96)( 13, 98)( 14, 97)( 15, 79)( 16, 80)( 17, 82)( 18, 81)
( 19, 75)( 20, 76)( 21, 78)( 22, 77)( 23, 83)( 24, 84)( 25, 86)( 26, 85)
( 27,103)( 28,104)( 29,106)( 30,105)( 31, 99)( 32,100)( 33,102)( 34,101)
( 35,107)( 36,108)( 37,110)( 38,109)( 39,127)( 40,128)( 41,130)( 42,129)
( 43,123)( 44,124)( 45,126)( 46,125)( 47,131)( 48,132)( 49,134)( 50,133)
( 51,115)( 52,116)( 53,118)( 54,117)( 55,111)( 56,112)( 57,114)( 58,113)
( 59,119)( 60,120)( 61,122)( 62,121)( 63,139)( 64,140)( 65,142)( 66,141)
( 67,135)( 68,136)( 69,138)( 70,137)( 71,143)( 72,144)( 73,146)( 74,145);;
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, 78)( 79, 82)
( 83, 86)( 87,102)( 88,100)( 89,101)( 90, 99)( 91,106)( 92,104)( 93,105)
( 94,103)( 95,110)( 96,108)( 97,109)( 98,107)(111,114)(115,118)(119,122)
(123,138)(124,136)(125,137)(126,135)(127,142)(128,140)(129,141)(130,139)
(131,146)(132,144)(133,145)(134,143);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
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, 
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)(  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)( 75,111)( 76,113)( 77,112)( 78,114)( 79,119)
( 80,121)( 81,120)( 82,122)( 83,115)( 84,117)( 85,116)( 86,118)( 87,135)
( 88,137)( 89,136)( 90,138)( 91,143)( 92,145)( 93,144)( 94,146)( 95,139)
( 96,141)( 97,140)( 98,142)( 99,123)(100,125)(101,124)(102,126)(103,131)
(104,133)(105,132)(106,134)(107,127)(108,129)(109,128)(110,130);
s2 := Sym(146)!(  3, 91)(  4, 92)(  5, 94)(  6, 93)(  7, 87)(  8, 88)(  9, 90)
( 10, 89)( 11, 95)( 12, 96)( 13, 98)( 14, 97)( 15, 79)( 16, 80)( 17, 82)
( 18, 81)( 19, 75)( 20, 76)( 21, 78)( 22, 77)( 23, 83)( 24, 84)( 25, 86)
( 26, 85)( 27,103)( 28,104)( 29,106)( 30,105)( 31, 99)( 32,100)( 33,102)
( 34,101)( 35,107)( 36,108)( 37,110)( 38,109)( 39,127)( 40,128)( 41,130)
( 42,129)( 43,123)( 44,124)( 45,126)( 46,125)( 47,131)( 48,132)( 49,134)
( 50,133)( 51,115)( 52,116)( 53,118)( 54,117)( 55,111)( 56,112)( 57,114)
( 58,113)( 59,119)( 60,120)( 61,122)( 62,121)( 63,139)( 64,140)( 65,142)
( 66,141)( 67,135)( 68,136)( 69,138)( 70,137)( 71,143)( 72,144)( 73,146)
( 74,145);
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, 78)
( 79, 82)( 83, 86)( 87,102)( 88,100)( 89,101)( 90, 99)( 91,106)( 92,104)
( 93,105)( 94,103)( 95,110)( 96,108)( 97,109)( 98,107)(111,114)(115,118)
(119,122)(123,138)(124,136)(125,137)(126,135)(127,142)(128,140)(129,141)
(130,139)(131,146)(132,144)(133,145)(134,143);
poly := sub<Sym(146)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
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, 
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