Polytope of Type {12,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,24}*1152d
if this polytope has a name.
Group : SmallGroup(1152,32543)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 24, 288, 48
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 :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,12}*576c
   3-fold quotients : {12,8}*384b
   4-fold quotients : {12,12}*288c
   6-fold quotients : {12,4}*192a
   8-fold quotients : {12,6}*144b, {6,12}*144c
   9-fold quotients : {4,8}*128b
   12-fold quotients : {12,4}*96a
   16-fold quotients : {6,6}*72c
   18-fold quotients : {4,4}*64
   24-fold quotients : {12,2}*48, {6,4}*48a
   32-fold quotients : {3,6}*36
   36-fold quotients : {4,4}*32
   48-fold quotients : {6,2}*24
   72-fold quotients : {2,4}*16, {4,2}*16
   96-fold quotients : {3,2}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 2.
      24 facets:
         24 of {12}*24
      12 vertex figures:
         12 of {24}*48

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

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