Polytope of Type {12,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*576e
if this polytope has a name.
Group : SmallGroup(576,8312)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 24, 144, 24
Order of s0s1s2 : 12
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {12,12,2} of size 1152
Vertex Figure Of :
   {2,12,12} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,12}*288b
   3-fold quotients : {12,4}*192b
   4-fold quotients : {12,6}*144b, {3,12}*144
   6-fold quotients : {12,4}*96b, {12,4}*96c, {6,4}*96
   8-fold quotients : {6,6}*72c
   12-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
   16-fold quotients : {3,6}*36
   24-fold quotients : {3,4}*24, {6,2}*24
   36-fold quotients : {4,2}*16
   48-fold quotients : {3,2}*12
   72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,24}*1152j, {12,24}*1152l, {24,12}*1152p, {24,12}*1152r, {12,12}*1152m
   3-fold covers : {36,12}*1728f, {12,12}*1728i, {12,12}*1728v
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2> of order 2.
      12 facets:
         12 of {12}*24
      16 vertex figures:
         8 of {6}*12
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1> of order 2.
      12 facets:
         12 of {12}*24
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 2.
      12 facets:
         12 of {12}*24
      12 vertex figures:
         12 of {12}*24

Permutation Representation (GAP) : 
s0 := (  2,  3)(  5,  9)(  6, 11)(  7, 10)(  8, 12)( 13, 25)( 14, 27)( 15, 26)( 16, 28)( 17, 33)( 18, 35)( 19, 34)( 20, 36)( 21, 29)( 22, 31)( 23, 30)( 24, 32)( 38, 39)( 41, 45)( 42, 47)( 43, 46)( 44, 48)( 49, 61)( 50, 63)( 51, 62)( 52, 64)( 53, 69)( 54, 71)( 55, 70)( 56, 72)( 57, 65)( 58, 67)( 59, 66)( 60, 68)( 73,109)( 74,111)( 75,110)( 76,112)( 77,117)( 78,119)( 79,118)( 80,120)( 81,113)( 82,115)( 83,114)( 84,116)( 85,133)( 86,135)( 87,134)( 88,136)( 89,141)( 90,143)( 91,142)( 92,144)( 93,137)( 94,139)( 95,138)( 96,140)( 97,121)( 98,123)( 99,122)(100,124)(101,129)(102,131)(103,130)(104,132)(105,125)(106,127)(107,126)(108,128);;
s1 := (  1, 89)(  2, 90)(  3, 92)(  4, 91)(  5, 85)(  6, 86)(  7, 88)(  8, 87)(  9, 93)( 10, 94)( 11, 96)( 12, 95)( 13, 77)( 14, 78)( 15, 80)( 16, 79)( 17, 73)( 18, 74)( 19, 76)( 20, 75)( 21, 81)( 22, 82)( 23, 84)( 24, 83)( 25,101)( 26,102)( 27,104)( 28,103)( 29, 97)( 30, 98)( 31,100)( 32, 99)( 33,105)( 34,106)( 35,108)( 36,107)( 37,125)( 38,126)( 39,128)( 40,127)( 41,121)( 42,122)( 43,124)( 44,123)( 45,129)( 46,130)( 47,132)( 48,131)( 49,113)( 50,114)( 51,116)( 52,115)( 53,109)( 54,110)( 55,112)( 56,111)( 57,117)( 58,118)( 59,120)( 60,119)( 61,137)( 62,138)( 63,140)( 64,139)( 65,133)( 66,134)( 67,136)( 68,135)( 69,141)( 70,142)( 71,144)( 72,143);;
s2 := (  1,  4)(  2,  3)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 13, 16)( 14, 15)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 25, 28)( 26, 27)( 29, 36)( 30, 35)( 31, 34)( 32, 33)( 37, 40)( 38, 39)( 41, 48)( 42, 47)( 43, 46)( 44, 45)( 49, 52)( 50, 51)( 53, 60)( 54, 59)( 55, 58)( 56, 57)( 61, 64)( 62, 63)( 65, 72)( 66, 71)( 67, 70)( 68, 69)( 73, 76)( 74, 75)( 77, 84)( 78, 83)( 79, 82)( 80, 81)( 85, 88)( 86, 87)( 89, 96)( 90, 95)( 91, 94)( 92, 93)( 97,100)( 98, 99)(101,108)(102,107)(103,106)(104,105)(109,112)(110,111)(113,120)(114,119)(115,118)(116,117)(121,124)(122,123)(125,132)(126,131)(127,130)(128,129)(133,136)(134,135)(137,144)(138,143)(139,142)(140,141);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(144)!(  2,  3)(  5,  9)(  6, 11)(  7, 10)(  8, 12)( 13, 25)( 14, 27)( 15, 26)( 16, 28)( 17, 33)( 18, 35)( 19, 34)( 20, 36)( 21, 29)( 22, 31)( 23, 30)( 24, 32)( 38, 39)( 41, 45)( 42, 47)( 43, 46)( 44, 48)( 49, 61)( 50, 63)( 51, 62)( 52, 64)( 53, 69)( 54, 71)( 55, 70)( 56, 72)( 57, 65)( 58, 67)( 59, 66)( 60, 68)( 73,109)( 74,111)( 75,110)( 76,112)( 77,117)( 78,119)( 79,118)( 80,120)( 81,113)( 82,115)( 83,114)( 84,116)( 85,133)( 86,135)( 87,134)( 88,136)( 89,141)( 90,143)( 91,142)( 92,144)( 93,137)( 94,139)( 95,138)( 96,140)( 97,121)( 98,123)( 99,122)(100,124)(101,129)(102,131)(103,130)(104,132)(105,125)(106,127)(107,126)(108,128);
s1 := Sym(144)!(  1, 89)(  2, 90)(  3, 92)(  4, 91)(  5, 85)(  6, 86)(  7, 88)(  8, 87)(  9, 93)( 10, 94)( 11, 96)( 12, 95)( 13, 77)( 14, 78)( 15, 80)( 16, 79)( 17, 73)( 18, 74)( 19, 76)( 20, 75)( 21, 81)( 22, 82)( 23, 84)( 24, 83)( 25,101)( 26,102)( 27,104)( 28,103)( 29, 97)( 30, 98)( 31,100)( 32, 99)( 33,105)( 34,106)( 35,108)( 36,107)( 37,125)( 38,126)( 39,128)( 40,127)( 41,121)( 42,122)( 43,124)( 44,123)( 45,129)( 46,130)( 47,132)( 48,131)( 49,113)( 50,114)( 51,116)( 52,115)( 53,109)( 54,110)( 55,112)( 56,111)( 57,117)( 58,118)( 59,120)( 60,119)( 61,137)( 62,138)( 63,140)( 64,139)( 65,133)( 66,134)( 67,136)( 68,135)( 69,141)( 70,142)( 71,144)( 72,143);
s2 := Sym(144)!(  1,  4)(  2,  3)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 13, 16)( 14, 15)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 25, 28)( 26, 27)( 29, 36)( 30, 35)( 31, 34)( 32, 33)( 37, 40)( 38, 39)( 41, 48)( 42, 47)( 43, 46)( 44, 45)( 49, 52)( 50, 51)( 53, 60)( 54, 59)( 55, 58)( 56, 57)( 61, 64)( 62, 63)( 65, 72)( 66, 71)( 67, 70)( 68, 69)( 73, 76)( 74, 75)( 77, 84)( 78, 83)( 79, 82)( 80, 81)( 85, 88)( 86, 87)( 89, 96)( 90, 95)( 91, 94)( 92, 93)( 97,100)( 98, 99)(101,108)(102,107)(103,106)(104,105)(109,112)(110,111)(113,120)(114,119)(115,118)(116,117)(121,124)(122,123)(125,132)(126,131)(127,130)(128,129)(133,136)(134,135)(137,144)(138,143)(139,142)(140,141);
poly := sub<Sym(144)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
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