Polytope of Type {51,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {51,6}*1836
if this polytope has a name.
Group : SmallGroup(1836,53)
Rank : 3
Schlafli Type : {51,6}
Number of vertices, edges, etc : 153, 459, 18
Order of s0s1s2 : 102
Order of s0s1s2s1 : 6
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) :
   3-fold quotients : {51,6}*612
   9-fold quotients : {51,2}*204
   17-fold quotients : {3,6}*108
   27-fold quotients : {17,2}*68
   51-fold quotients : {3,6}*36
   153-fold quotients : {3,2}*12
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*s1*s2*s1> of order 3.
      6 facets:
         6 of {51}*102
      85 vertex figures:
         34 of {6}*12
         51 of {2}*4

Permutation Representation (GAP) : 
s0 := (  4, 49)(  5, 50)(  6, 51)(  7, 46)(  8, 47)(  9, 48)( 10, 43)( 11, 44)( 12, 45)( 13, 40)( 14, 41)( 15, 42)( 16, 37)( 17, 38)( 18, 39)( 19, 34)( 20, 35)( 21, 36)( 22, 31)( 23, 32)( 24, 33)( 25, 28)( 26, 29)( 27, 30)( 52,103)( 53,104)( 54,105)( 55,151)( 56,152)( 57,153)( 58,148)( 59,149)( 60,150)( 61,145)( 62,146)( 63,147)( 64,142)( 65,143)( 66,144)( 67,139)( 68,140)( 69,141)( 70,136)( 71,137)( 72,138)( 73,133)( 74,134)( 75,135)( 76,130)( 77,131)( 78,132)( 79,127)( 80,128)( 81,129)( 82,124)( 83,125)( 84,126)( 85,121)( 86,122)( 87,123)( 88,118)( 89,119)( 90,120)( 91,115)( 92,116)( 93,117)( 94,112)( 95,113)( 96,114)( 97,109)( 98,110)( 99,111)(100,106)(101,107)(102,108);;
s1 := (  1, 56)(  2, 57)(  3, 55)(  4, 53)(  5, 54)(  6, 52)(  7,101)(  8,102)(  9,100)( 10, 98)( 11, 99)( 12, 97)( 13, 95)( 14, 96)( 15, 94)( 16, 92)( 17, 93)( 18, 91)( 19, 89)( 20, 90)( 21, 88)( 22, 86)( 23, 87)( 24, 85)( 25, 83)( 26, 84)( 27, 82)( 28, 80)( 29, 81)( 30, 79)( 31, 77)( 32, 78)( 33, 76)( 34, 74)( 35, 75)( 36, 73)( 37, 71)( 38, 72)( 39, 70)( 40, 68)( 41, 69)( 42, 67)( 43, 65)( 44, 66)( 45, 64)( 46, 62)( 47, 63)( 48, 61)( 49, 59)( 50, 60)( 51, 58)(103,106)(104,107)(105,108)(109,151)(110,152)(111,153)(112,148)(113,149)(114,150)(115,145)(116,146)(117,147)(118,142)(119,143)(120,144)(121,139)(122,140)(123,141)(124,136)(125,137)(126,138)(127,133)(128,134)(129,135);;
s2 := (  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)( 50, 51)( 52,103)( 53,105)( 54,104)( 55,106)( 56,108)( 57,107)( 58,109)( 59,111)( 60,110)( 61,112)( 62,114)( 63,113)( 64,115)( 65,117)( 66,116)( 67,118)( 68,120)( 69,119)( 70,121)( 71,123)( 72,122)( 73,124)( 74,126)( 75,125)( 76,127)( 77,129)( 78,128)( 79,130)( 80,132)( 81,131)( 82,133)( 83,135)( 84,134)( 85,136)( 86,138)( 87,137)( 88,139)( 89,141)( 90,140)( 91,142)( 92,144)( 93,143)( 94,145)( 95,147)( 96,146)( 97,148)( 98,150)( 99,149)(100,151)(101,153)(102,152);;
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*s2*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0, 
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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(153)!(  4, 49)(  5, 50)(  6, 51)(  7, 46)(  8, 47)(  9, 48)( 10, 43)( 11, 44)( 12, 45)( 13, 40)( 14, 41)( 15, 42)( 16, 37)( 17, 38)( 18, 39)( 19, 34)( 20, 35)( 21, 36)( 22, 31)( 23, 32)( 24, 33)( 25, 28)( 26, 29)( 27, 30)( 52,103)( 53,104)( 54,105)( 55,151)( 56,152)( 57,153)( 58,148)( 59,149)( 60,150)( 61,145)( 62,146)( 63,147)( 64,142)( 65,143)( 66,144)( 67,139)( 68,140)( 69,141)( 70,136)( 71,137)( 72,138)( 73,133)( 74,134)( 75,135)( 76,130)( 77,131)( 78,132)( 79,127)( 80,128)( 81,129)( 82,124)( 83,125)( 84,126)( 85,121)( 86,122)( 87,123)( 88,118)( 89,119)( 90,120)( 91,115)( 92,116)( 93,117)( 94,112)( 95,113)( 96,114)( 97,109)( 98,110)( 99,111)(100,106)(101,107)(102,108);
s1 := Sym(153)!(  1, 56)(  2, 57)(  3, 55)(  4, 53)(  5, 54)(  6, 52)(  7,101)(  8,102)(  9,100)( 10, 98)( 11, 99)( 12, 97)( 13, 95)( 14, 96)( 15, 94)( 16, 92)( 17, 93)( 18, 91)( 19, 89)( 20, 90)( 21, 88)( 22, 86)( 23, 87)( 24, 85)( 25, 83)( 26, 84)( 27, 82)( 28, 80)( 29, 81)( 30, 79)( 31, 77)( 32, 78)( 33, 76)( 34, 74)( 35, 75)( 36, 73)( 37, 71)( 38, 72)( 39, 70)( 40, 68)( 41, 69)( 42, 67)( 43, 65)( 44, 66)( 45, 64)( 46, 62)( 47, 63)( 48, 61)( 49, 59)( 50, 60)( 51, 58)(103,106)(104,107)(105,108)(109,151)(110,152)(111,153)(112,148)(113,149)(114,150)(115,145)(116,146)(117,147)(118,142)(119,143)(120,144)(121,139)(122,140)(123,141)(124,136)(125,137)(126,138)(127,133)(128,134)(129,135);
s2 := Sym(153)!(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)( 50, 51)( 52,103)( 53,105)( 54,104)( 55,106)( 56,108)( 57,107)( 58,109)( 59,111)( 60,110)( 61,112)( 62,114)( 63,113)( 64,115)( 65,117)( 66,116)( 67,118)( 68,120)( 69,119)( 70,121)( 71,123)( 72,122)( 73,124)( 74,126)( 75,125)( 76,127)( 77,129)( 78,128)( 79,130)( 80,132)( 81,131)( 82,133)( 83,135)( 84,134)( 85,136)( 86,138)( 87,137)( 88,139)( 89,141)( 90,140)( 91,142)( 92,144)( 93,143)( 94,145)( 95,147)( 96,146)( 97,148)( 98,150)( 99,149)(100,151)(101,153)(102,152);
poly := sub<Sym(153)|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*s2*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0, 
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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
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