Polytope of Type {12,10}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,10}*1200c
if this polytope has a name.
Group : SmallGroup(1200,1002)
Rank : 3
Schlafli Type : {12,10}
Number of vertices, edges, etc : 60, 300, 50
Order of s0s1s2 : 12
Order of s0s1s2s1 : 10
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 : {12,10}*600
   3-fold quotients : {4,10}*400
   6-fold quotients : {4,10}*200
   25-fold quotients : {12,2}*48
   50-fold quotients : {6,2}*24
   75-fold quotients : {4,2}*16
   100-fold quotients : {3,2}*12
   150-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*s2*s1*s2*s1*s0*s1*s2*s1> of order 5.
      10 facets:
         10 of {12}*24
      12 vertex figures:
         12 of {10}*20
   P/N, where N=<s1*s2*s1*s2> of order 5.
      10 facets:
         10 of {12}*24
      36 vertex figures:
         30 of {2}*4
         6 of {10}*20
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 5.
      10 facets:
         10 of {12}*24
      12 vertex figures:
         12 of {10}*20

Permutation Representation (GAP) : 
s0 := (  2, 12)(  3, 23)(  4,  9)(  5, 20)(  6, 21)(  8, 18)( 10, 15)( 11, 16)( 14, 24)( 17, 22)( 26, 51)( 27, 62)( 28, 73)( 29, 59)( 30, 70)( 31, 71)( 32, 57)( 33, 68)( 34, 54)( 35, 65)( 36, 66)( 37, 52)( 38, 63)( 39, 74)( 40, 60)( 41, 61)( 42, 72)( 43, 58)( 44, 69)( 45, 55)( 46, 56)( 47, 67)( 48, 53)( 49, 64)( 50, 75)( 77, 87)( 78, 98)( 79, 84)( 80, 95)( 81, 96)( 83, 93)( 85, 90)( 86, 91)( 89, 99)( 92, 97)(101,126)(102,137)(103,148)(104,134)(105,145)(106,146)(107,132)(108,143)(109,129)(110,140)(111,141)(112,127)(113,138)(114,149)(115,135)(116,136)(117,147)(118,133)(119,144)(120,130)(121,131)(122,142)(123,128)(124,139)(125,150);;
s1 := (  1, 26)(  2, 34)(  3, 37)(  4, 45)(  5, 48)(  6, 38)(  7, 41)(  8, 49)(  9, 27)( 10, 35)( 11, 50)( 12, 28)( 13, 31)( 14, 39)( 15, 42)( 16, 32)( 17, 40)( 18, 43)( 19, 46)( 20, 29)( 21, 44)( 22, 47)( 23, 30)( 24, 33)( 25, 36)( 52, 59)( 53, 62)( 54, 70)( 55, 73)( 56, 63)( 57, 66)( 58, 74)( 61, 75)( 65, 67)( 69, 71)( 76,101)( 77,109)( 78,112)( 79,120)( 80,123)( 81,113)( 82,116)( 83,124)( 84,102)( 85,110)( 86,125)( 87,103)( 88,106)( 89,114)( 90,117)( 91,107)( 92,115)( 93,118)( 94,121)( 95,104)( 96,119)( 97,122)( 98,105)( 99,108)(100,111)(127,134)(128,137)(129,145)(130,148)(131,138)(132,141)(133,149)(136,150)(140,142)(144,146);;
s2 := (  1, 82)(  2, 81)(  3, 85)(  4, 84)(  5, 83)(  6, 77)(  7, 76)(  8, 80)(  9, 79)( 10, 78)( 11, 97)( 12, 96)( 13,100)( 14, 99)( 15, 98)( 16, 92)( 17, 91)( 18, 95)( 19, 94)( 20, 93)( 21, 87)( 22, 86)( 23, 90)( 24, 89)( 25, 88)( 26,107)( 27,106)( 28,110)( 29,109)( 30,108)( 31,102)( 32,101)( 33,105)( 34,104)( 35,103)( 36,122)( 37,121)( 38,125)( 39,124)( 40,123)( 41,117)( 42,116)( 43,120)( 44,119)( 45,118)( 46,112)( 47,111)( 48,115)( 49,114)( 50,113)( 51,132)( 52,131)( 53,135)( 54,134)( 55,133)( 56,127)( 57,126)( 58,130)( 59,129)( 60,128)( 61,147)( 62,146)( 63,150)( 64,149)( 65,148)( 66,142)( 67,141)( 68,145)( 69,144)( 70,143)( 71,137)( 72,136)( 73,140)( 74,139)( 75,138);;
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*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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(150)!(  2, 12)(  3, 23)(  4,  9)(  5, 20)(  6, 21)(  8, 18)( 10, 15)( 11, 16)( 14, 24)( 17, 22)( 26, 51)( 27, 62)( 28, 73)( 29, 59)( 30, 70)( 31, 71)( 32, 57)( 33, 68)( 34, 54)( 35, 65)( 36, 66)( 37, 52)( 38, 63)( 39, 74)( 40, 60)( 41, 61)( 42, 72)( 43, 58)( 44, 69)( 45, 55)( 46, 56)( 47, 67)( 48, 53)( 49, 64)( 50, 75)( 77, 87)( 78, 98)( 79, 84)( 80, 95)( 81, 96)( 83, 93)( 85, 90)( 86, 91)( 89, 99)( 92, 97)(101,126)(102,137)(103,148)(104,134)(105,145)(106,146)(107,132)(108,143)(109,129)(110,140)(111,141)(112,127)(113,138)(114,149)(115,135)(116,136)(117,147)(118,133)(119,144)(120,130)(121,131)(122,142)(123,128)(124,139)(125,150);
s1 := Sym(150)!(  1, 26)(  2, 34)(  3, 37)(  4, 45)(  5, 48)(  6, 38)(  7, 41)(  8, 49)(  9, 27)( 10, 35)( 11, 50)( 12, 28)( 13, 31)( 14, 39)( 15, 42)( 16, 32)( 17, 40)( 18, 43)( 19, 46)( 20, 29)( 21, 44)( 22, 47)( 23, 30)( 24, 33)( 25, 36)( 52, 59)( 53, 62)( 54, 70)( 55, 73)( 56, 63)( 57, 66)( 58, 74)( 61, 75)( 65, 67)( 69, 71)( 76,101)( 77,109)( 78,112)( 79,120)( 80,123)( 81,113)( 82,116)( 83,124)( 84,102)( 85,110)( 86,125)( 87,103)( 88,106)( 89,114)( 90,117)( 91,107)( 92,115)( 93,118)( 94,121)( 95,104)( 96,119)( 97,122)( 98,105)( 99,108)(100,111)(127,134)(128,137)(129,145)(130,148)(131,138)(132,141)(133,149)(136,150)(140,142)(144,146);
s2 := Sym(150)!(  1, 82)(  2, 81)(  3, 85)(  4, 84)(  5, 83)(  6, 77)(  7, 76)(  8, 80)(  9, 79)( 10, 78)( 11, 97)( 12, 96)( 13,100)( 14, 99)( 15, 98)( 16, 92)( 17, 91)( 18, 95)( 19, 94)( 20, 93)( 21, 87)( 22, 86)( 23, 90)( 24, 89)( 25, 88)( 26,107)( 27,106)( 28,110)( 29,109)( 30,108)( 31,102)( 32,101)( 33,105)( 34,104)( 35,103)( 36,122)( 37,121)( 38,125)( 39,124)( 40,123)( 41,117)( 42,116)( 43,120)( 44,119)( 45,118)( 46,112)( 47,111)( 48,115)( 49,114)( 50,113)( 51,132)( 52,131)( 53,135)( 54,134)( 55,133)( 56,127)( 57,126)( 58,130)( 59,129)( 60,128)( 61,147)( 62,146)( 63,150)( 64,149)( 65,148)( 66,142)( 67,141)( 68,145)( 69,144)( 70,143)( 71,137)( 72,136)( 73,140)( 74,139)( 75,138);
poly := sub<Sym(150)|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*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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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