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}*576a
if this polytope has a name.
Group : SmallGroup(576,2292)
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
   Self-Dual
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 : {12,12}*288a
   3-fold quotients : {4,12}*192a, {12,4}*192a
   4-fold quotients : {6,12}*144a, {12,6}*144a
   6-fold quotients : {4,12}*96a, {12,4}*96a
   8-fold quotients : {6,6}*72a
   9-fold quotients : {4,4}*64
   12-fold quotients : {2,12}*48, {12,2}*48, {4,6}*48a, {6,4}*48a
   18-fold quotients : {4,4}*32
   24-fold quotients : {2,6}*24, {6,2}*24
   36-fold quotients : {2,4}*16, {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}*1152b, {24,12}*1152b, {12,24}*1152e, {24,12}*1152e, {12,12}*1152c
   3-fold covers : {12,36}*1728a, {36,12}*1728a, {12,12}*1728c, {12,12}*1728h
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 2.
      18 facets:
         12 of {6}*12
         6 of {12}*24
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      12 facets:
         12 of {12}*24
      18 vertex figures:
         12 of {6}*12
         6 of {12}*24

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