Polytope of Type {4,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24}*1152b
if this polytope has a name.
Group : SmallGroup(1152,32554)
Rank : 3
Schlafli Type : {4,24}
Number of vertices, edges, etc : 24, 288, 144
Order of s0s1s2 : 4
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
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 : {4,12}*576
   4-fold quotients : {4,12}*288
   8-fold quotients : {4,6}*144
   9-fold quotients : {4,8}*128b
   16-fold quotients : {4,6}*72
   18-fold quotients : {4,4}*64
   36-fold quotients : {4,4}*32
   72-fold quotients : {2,4}*16, {4,2}*16
   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=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      72 facets:
         72 of {4}*8
      12 vertex figures:
         12 of {24}*48
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2> of order 3.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         4 of {24}*48
         12 of {8}*16
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 3.
      48 facets:
         48 of {4}*8
      8 vertex figures:
         8 of {24}*48
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 4.
      36 facets:
         36 of {4}*8
      6 vertex figures:
         6 of {24}*48
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      36 facets:
         36 of {4}*8
      6 vertex figures:
         6 of {24}*48
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 6.
      24 facets:
         24 of {4}*8
      4 vertex figures:
         4 of {24}*48
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 6.
      24 facets:
         24 of {4}*8
      4 vertex figures:
         4 of {24}*48
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 6.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         2 of {24}*48
         6 of {8}*16

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