Polytope of Type {10,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12}*1200c
if this polytope has a name.
Group : SmallGroup(1200,1002)
Rank : 3
Schlafli Type : {10,12}
Number of vertices, edges, etc : 50, 300, 60
Order of s0s1s2 : 12
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,12}*600
   3-fold quotients : {10,4}*400
   6-fold quotients : {10,4}*200
   25-fold quotients : {2,12}*48
   50-fold quotients : {2,6}*24
   75-fold quotients : {2,4}*16
   100-fold quotients : {2,3}*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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1> of order 5.
      12 facets:
         12 of {10}*20
      10 vertex figures:
         10 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 5.
      12 facets:
         12 of {10}*20
      10 vertex figures:
         10 of {12}*24
   P/N, where N=<s0*s1*s0*s1> of order 5.
      36 facets:
         30 of {2}*4
         6 of {10}*20
      10 vertex figures:
         10 of {12}*24

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