Polytope of Type {2,12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,12}*1152a
if this polytope has a name.
Group : SmallGroup(1152,99274)
Rank : 4
Schlafli Type : {2,12,12}
Number of vertices, edges, etc : 2, 24, 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 : {2,12,12}*576a
   3-fold quotients : {2,4,12}*384a, {2,12,4}*384a
   4-fold quotients : {2,6,12}*288a, {2,12,6}*288a
   6-fold quotients : {2,4,12}*192a, {2,12,4}*192a
   8-fold quotients : {2,6,6}*144a
   9-fold quotients : {2,4,4}*128
   12-fold quotients : {2,2,12}*96, {2,12,2}*96, {2,4,6}*96a, {2,6,4}*96a
   18-fold quotients : {2,4,4}*64
   24-fold quotients : {2,2,6}*48, {2,6,2}*48
   36-fold quotients : {2,2,4}*32, {2,4,2}*32
   48-fold quotients : {2,2,3}*24, {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,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 39, 48)( 40, 50)( 41, 49)( 42, 51)
( 43, 53)( 44, 52)( 45, 54)( 46, 56)( 47, 55)( 57, 66)( 58, 68)( 59, 67)
( 60, 69)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 75, 93)( 76, 95)
( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 99)( 82,101)( 83,100)( 84,102)
( 85,104)( 86,103)( 87,105)( 88,107)( 89,106)( 90,108)( 91,110)( 92,109)
(111,138)(112,140)(113,139)(114,141)(115,143)(116,142)(117,144)(118,146)
(119,145)(120,129)(121,131)(122,130)(123,132)(124,134)(125,133)(126,135)
(127,137)(128,136);;
s2 := (  3, 76)(  4, 75)(  5, 77)(  6, 82)(  7, 81)(  8, 83)(  9, 79)( 10, 78)
( 11, 80)( 12, 85)( 13, 84)( 14, 86)( 15, 91)( 16, 90)( 17, 92)( 18, 88)
( 19, 87)( 20, 89)( 21, 94)( 22, 93)( 23, 95)( 24,100)( 25, 99)( 26,101)
( 27, 97)( 28, 96)( 29, 98)( 30,103)( 31,102)( 32,104)( 33,109)( 34,108)
( 35,110)( 36,106)( 37,105)( 38,107)( 39,112)( 40,111)( 41,113)( 42,118)
( 43,117)( 44,119)( 45,115)( 46,114)( 47,116)( 48,121)( 49,120)( 50,122)
( 51,127)( 52,126)( 53,128)( 54,124)( 55,123)( 56,125)( 57,130)( 58,129)
( 59,131)( 60,136)( 61,135)( 62,137)( 63,133)( 64,132)( 65,134)( 66,139)
( 67,138)( 68,140)( 69,145)( 70,144)( 71,146)( 72,142)( 73,141)( 74,143);;
s3 := (  3,  6)(  4,  7)(  5,  8)( 12, 15)( 13, 16)( 14, 17)( 21, 33)( 22, 34)
( 23, 35)( 24, 30)( 25, 31)( 26, 32)( 27, 36)( 28, 37)( 29, 38)( 39, 42)
( 40, 43)( 41, 44)( 48, 51)( 49, 52)( 50, 53)( 57, 69)( 58, 70)( 59, 71)
( 60, 66)( 61, 67)( 62, 68)( 63, 72)( 64, 73)( 65, 74)( 75,114)( 76,115)
( 77,116)( 78,111)( 79,112)( 80,113)( 81,117)( 82,118)( 83,119)( 84,123)
( 85,124)( 86,125)( 87,120)( 88,121)( 89,122)( 90,126)( 91,127)( 92,128)
( 93,141)( 94,142)( 95,143)( 96,138)( 97,139)( 98,140)( 99,144)(100,145)
(101,146)(102,132)(103,133)(104,134)(105,129)(106,130)(107,131)(108,135)
(109,136)(110,137);;
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, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*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*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope