Polytope of Type {36,10}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,10}*720
Also Known As : {36,10|2}. if this polytope has another name.
Group : SmallGroup(720,136)
Rank : 3
Schlafli Type : {36,10}
Number of vertices, edges, etc : 36, 180, 10
Order of s0s1s2 : 180
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {36,10,2} of size 1440
Vertex Figure Of :
   {2,36,10} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {18,10}*360
   3-fold quotients : {12,10}*240
   5-fold quotients : {36,2}*144
   6-fold quotients : {6,10}*120
   9-fold quotients : {4,10}*80
   10-fold quotients : {18,2}*72
   15-fold quotients : {12,2}*48
   18-fold quotients : {2,10}*40
   20-fold quotients : {9,2}*36
   30-fold quotients : {6,2}*24
   36-fold quotients : {2,5}*20
   45-fold quotients : {4,2}*16
   60-fold quotients : {3,2}*12
   90-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {72,10}*1440, {36,20}*1440
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) : 
s0 := (  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 16, 33)( 17, 32)( 18, 31)( 19, 36)( 20, 35)( 21, 34)( 22, 39)( 23, 38)( 24, 37)( 25, 42)( 26, 41)( 27, 40)( 28, 45)( 29, 44)( 30, 43)( 47, 48)( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 61, 78)( 62, 77)( 63, 76)( 64, 81)( 65, 80)( 66, 79)( 67, 84)( 68, 83)( 69, 82)( 70, 87)( 71, 86)( 72, 85)( 73, 90)( 74, 89)( 75, 88)( 91,136)( 92,138)( 93,137)( 94,139)( 95,141)( 96,140)( 97,142)( 98,144)( 99,143)(100,145)(101,147)(102,146)(103,148)(104,150)(105,149)(106,168)(107,167)(108,166)(109,171)(110,170)(111,169)(112,174)(113,173)(114,172)(115,177)(116,176)(117,175)(118,180)(119,179)(120,178)(121,153)(122,152)(123,151)(124,156)(125,155)(126,154)(127,159)(128,158)(129,157)(130,162)(131,161)(132,160)(133,165)(134,164)(135,163);;
s1 := (  1,106)(  2,108)(  3,107)(  4,118)(  5,120)(  6,119)(  7,115)(  8,117)(  9,116)( 10,112)( 11,114)( 12,113)( 13,109)( 14,111)( 15,110)( 16, 91)( 17, 93)( 18, 92)( 19,103)( 20,105)( 21,104)( 22,100)( 23,102)( 24,101)( 25, 97)( 26, 99)( 27, 98)( 28, 94)( 29, 96)( 30, 95)( 31,123)( 32,122)( 33,121)( 34,135)( 35,134)( 36,133)( 37,132)( 38,131)( 39,130)( 40,129)( 41,128)( 42,127)( 43,126)( 44,125)( 45,124)( 46,151)( 47,153)( 48,152)( 49,163)( 50,165)( 51,164)( 52,160)( 53,162)( 54,161)( 55,157)( 56,159)( 57,158)( 58,154)( 59,156)( 60,155)( 61,136)( 62,138)( 63,137)( 64,148)( 65,150)( 66,149)( 67,145)( 68,147)( 69,146)( 70,142)( 71,144)( 72,143)( 73,139)( 74,141)( 75,140)( 76,168)( 77,167)( 78,166)( 79,180)( 80,179)( 81,178)( 82,177)( 83,176)( 84,175)( 85,174)( 86,173)( 87,172)( 88,171)( 89,170)( 90,169);;
s2 := (  1,  4)(  2,  5)(  3,  6)(  7, 13)(  8, 14)(  9, 15)( 16, 19)( 17, 20)( 18, 21)( 22, 28)( 23, 29)( 24, 30)( 31, 34)( 32, 35)( 33, 36)( 37, 43)( 38, 44)( 39, 45)( 46, 49)( 47, 50)( 48, 51)( 52, 58)( 53, 59)( 54, 60)( 61, 64)( 62, 65)( 63, 66)( 67, 73)( 68, 74)( 69, 75)( 76, 79)( 77, 80)( 78, 81)( 82, 88)( 83, 89)( 84, 90)( 91, 94)( 92, 95)( 93, 96)( 97,103)( 98,104)( 99,105)(106,109)(107,110)(108,111)(112,118)(113,119)(114,120)(121,124)(122,125)(123,126)(127,133)(128,134)(129,135)(136,139)(137,140)(138,141)(142,148)(143,149)(144,150)(151,154)(152,155)(153,156)(157,163)(158,164)(159,165)(166,169)(167,170)(168,171)(172,178)(173,179)(174,180);;
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*s0*s1*s2*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*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(180)!(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 16, 33)( 17, 32)( 18, 31)( 19, 36)( 20, 35)( 21, 34)( 22, 39)( 23, 38)( 24, 37)( 25, 42)( 26, 41)( 27, 40)( 28, 45)( 29, 44)( 30, 43)( 47, 48)( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 61, 78)( 62, 77)( 63, 76)( 64, 81)( 65, 80)( 66, 79)( 67, 84)( 68, 83)( 69, 82)( 70, 87)( 71, 86)( 72, 85)( 73, 90)( 74, 89)( 75, 88)( 91,136)( 92,138)( 93,137)( 94,139)( 95,141)( 96,140)( 97,142)( 98,144)( 99,143)(100,145)(101,147)(102,146)(103,148)(104,150)(105,149)(106,168)(107,167)(108,166)(109,171)(110,170)(111,169)(112,174)(113,173)(114,172)(115,177)(116,176)(117,175)(118,180)(119,179)(120,178)(121,153)(122,152)(123,151)(124,156)(125,155)(126,154)(127,159)(128,158)(129,157)(130,162)(131,161)(132,160)(133,165)(134,164)(135,163);
s1 := Sym(180)!(  1,106)(  2,108)(  3,107)(  4,118)(  5,120)(  6,119)(  7,115)(  8,117)(  9,116)( 10,112)( 11,114)( 12,113)( 13,109)( 14,111)( 15,110)( 16, 91)( 17, 93)( 18, 92)( 19,103)( 20,105)( 21,104)( 22,100)( 23,102)( 24,101)( 25, 97)( 26, 99)( 27, 98)( 28, 94)( 29, 96)( 30, 95)( 31,123)( 32,122)( 33,121)( 34,135)( 35,134)( 36,133)( 37,132)( 38,131)( 39,130)( 40,129)( 41,128)( 42,127)( 43,126)( 44,125)( 45,124)( 46,151)( 47,153)( 48,152)( 49,163)( 50,165)( 51,164)( 52,160)( 53,162)( 54,161)( 55,157)( 56,159)( 57,158)( 58,154)( 59,156)( 60,155)( 61,136)( 62,138)( 63,137)( 64,148)( 65,150)( 66,149)( 67,145)( 68,147)( 69,146)( 70,142)( 71,144)( 72,143)( 73,139)( 74,141)( 75,140)( 76,168)( 77,167)( 78,166)( 79,180)( 80,179)( 81,178)( 82,177)( 83,176)( 84,175)( 85,174)( 86,173)( 87,172)( 88,171)( 89,170)( 90,169);
s2 := Sym(180)!(  1,  4)(  2,  5)(  3,  6)(  7, 13)(  8, 14)(  9, 15)( 16, 19)( 17, 20)( 18, 21)( 22, 28)( 23, 29)( 24, 30)( 31, 34)( 32, 35)( 33, 36)( 37, 43)( 38, 44)( 39, 45)( 46, 49)( 47, 50)( 48, 51)( 52, 58)( 53, 59)( 54, 60)( 61, 64)( 62, 65)( 63, 66)( 67, 73)( 68, 74)( 69, 75)( 76, 79)( 77, 80)( 78, 81)( 82, 88)( 83, 89)( 84, 90)( 91, 94)( 92, 95)( 93, 96)( 97,103)( 98,104)( 99,105)(106,109)(107,110)(108,111)(112,118)(113,119)(114,120)(121,124)(122,125)(123,126)(127,133)(128,134)(129,135)(136,139)(137,140)(138,141)(142,148)(143,149)(144,150)(151,154)(152,155)(153,156)(157,163)(158,164)(159,165)(166,169)(167,170)(168,171)(172,178)(173,179)(174,180);
poly := sub<Sym(180)|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*s0*s1*s2*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*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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