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}*576d
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 : 4
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}*288a
   3-fold quotients : {12,4}*192b
   4-fold quotients : {12,6}*144a, {6,12}*144d
   6-fold quotients : {12,4}*96b, {12,4}*96c, {6,4}*96
   8-fold quotients : {6,6}*72a
   12-fold quotients : {12,2}*48, {4,6}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   24-fold quotients : {3,4}*24, {2,6}*24, {6,2}*24
   36-fold quotients : {4,2}*16
   48-fold quotients : {2,3}*12, {3,2}*12
   72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,24}*1152i, {12,24}*1152k, {24,12}*1152o, {24,12}*1152q, {12,12}*1152k
   3-fold covers : {12,36}*1728c, {36,12}*1728e, {12,12}*1728j, {12,12}*1728v
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*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*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2> 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)(  6,  7)( 10, 11)( 13, 25)( 14, 27)( 15, 26)( 16, 28)( 17, 29)( 18, 31)( 19, 30)( 20, 32)( 21, 33)( 22, 35)( 23, 34)( 24, 36)( 38, 39)( 42, 43)( 46, 47)( 49, 61)( 50, 63)( 51, 62)( 52, 64)( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 69)( 58, 71)( 59, 70)( 60, 72)( 73,109)( 74,111)( 75,110)( 76,112)( 77,113)( 78,115)( 79,114)( 80,116)( 81,117)( 82,119)( 83,118)( 84,120)( 85,133)( 86,135)( 87,134)( 88,136)( 89,137)( 90,139)( 91,138)( 92,140)( 93,141)( 94,143)( 95,142)( 96,144)( 97,121)( 98,123)( 99,122)(100,124)(101,125)(102,127)(103,126)(104,128)(105,129)(106,131)(107,130)(108,132);;
s1 := (  1, 85)(  2, 86)(  3, 88)(  4, 87)(  5, 93)(  6, 94)(  7, 96)(  8, 95)(  9, 89)( 10, 90)( 11, 92)( 12, 91)( 13, 73)( 14, 74)( 15, 76)( 16, 75)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 77)( 22, 78)( 23, 80)( 24, 79)( 25, 97)( 26, 98)( 27,100)( 28, 99)( 29,105)( 30,106)( 31,108)( 32,107)( 33,101)( 34,102)( 35,104)( 36,103)( 37,121)( 38,122)( 39,124)( 40,123)( 41,129)( 42,130)( 43,132)( 44,131)( 45,125)( 46,126)( 47,128)( 48,127)( 49,109)( 50,110)( 51,112)( 52,111)( 53,117)( 54,118)( 55,120)( 56,119)( 57,113)( 58,114)( 59,116)( 60,115)( 61,133)( 62,134)( 63,136)( 64,135)( 65,141)( 66,142)( 67,144)( 68,143)( 69,137)( 70,138)( 71,140)( 72,139);;
s2 := (  1,  8)(  2,  7)(  3,  6)(  4,  5)(  9, 12)( 10, 11)( 13, 20)( 14, 19)( 15, 18)( 16, 17)( 21, 24)( 22, 23)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 33, 36)( 34, 35)( 37, 44)( 38, 43)( 39, 42)( 40, 41)( 45, 48)( 46, 47)( 49, 56)( 50, 55)( 51, 54)( 52, 53)( 57, 60)( 58, 59)( 61, 68)( 62, 67)( 63, 66)( 64, 65)( 69, 72)( 70, 71)( 73, 80)( 74, 79)( 75, 78)( 76, 77)( 81, 84)( 82, 83)( 85, 92)( 86, 91)( 87, 90)( 88, 89)( 93, 96)( 94, 95)( 97,104)( 98,103)( 99,102)(100,101)(105,108)(106,107)(109,116)(110,115)(111,114)(112,113)(117,120)(118,119)(121,128)(122,127)(123,126)(124,125)(129,132)(130,131)(133,140)(134,139)(135,138)(136,137)(141,144)(142,143);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*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)(  6,  7)( 10, 11)( 13, 25)( 14, 27)( 15, 26)( 16, 28)( 17, 29)( 18, 31)( 19, 30)( 20, 32)( 21, 33)( 22, 35)( 23, 34)( 24, 36)( 38, 39)( 42, 43)( 46, 47)( 49, 61)( 50, 63)( 51, 62)( 52, 64)( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 69)( 58, 71)( 59, 70)( 60, 72)( 73,109)( 74,111)( 75,110)( 76,112)( 77,113)( 78,115)( 79,114)( 80,116)( 81,117)( 82,119)( 83,118)( 84,120)( 85,133)( 86,135)( 87,134)( 88,136)( 89,137)( 90,139)( 91,138)( 92,140)( 93,141)( 94,143)( 95,142)( 96,144)( 97,121)( 98,123)( 99,122)(100,124)(101,125)(102,127)(103,126)(104,128)(105,129)(106,131)(107,130)(108,132);
s1 := Sym(144)!(  1, 85)(  2, 86)(  3, 88)(  4, 87)(  5, 93)(  6, 94)(  7, 96)(  8, 95)(  9, 89)( 10, 90)( 11, 92)( 12, 91)( 13, 73)( 14, 74)( 15, 76)( 16, 75)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 77)( 22, 78)( 23, 80)( 24, 79)( 25, 97)( 26, 98)( 27,100)( 28, 99)( 29,105)( 30,106)( 31,108)( 32,107)( 33,101)( 34,102)( 35,104)( 36,103)( 37,121)( 38,122)( 39,124)( 40,123)( 41,129)( 42,130)( 43,132)( 44,131)( 45,125)( 46,126)( 47,128)( 48,127)( 49,109)( 50,110)( 51,112)( 52,111)( 53,117)( 54,118)( 55,120)( 56,119)( 57,113)( 58,114)( 59,116)( 60,115)( 61,133)( 62,134)( 63,136)( 64,135)( 65,141)( 66,142)( 67,144)( 68,143)( 69,137)( 70,138)( 71,140)( 72,139);
s2 := Sym(144)!(  1,  8)(  2,  7)(  3,  6)(  4,  5)(  9, 12)( 10, 11)( 13, 20)( 14, 19)( 15, 18)( 16, 17)( 21, 24)( 22, 23)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 33, 36)( 34, 35)( 37, 44)( 38, 43)( 39, 42)( 40, 41)( 45, 48)( 46, 47)( 49, 56)( 50, 55)( 51, 54)( 52, 53)( 57, 60)( 58, 59)( 61, 68)( 62, 67)( 63, 66)( 64, 65)( 69, 72)( 70, 71)( 73, 80)( 74, 79)( 75, 78)( 76, 77)( 81, 84)( 82, 83)( 85, 92)( 86, 91)( 87, 90)( 88, 89)( 93, 96)( 94, 95)( 97,104)( 98,103)( 99,102)(100,101)(105,108)(106,107)(109,116)(110,115)(111,114)(112,113)(117,120)(118,119)(121,128)(122,127)(123,126)(124,125)(129,132)(130,131)(133,140)(134,139)(135,138)(136,137)(141,144)(142,143);
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*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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