Polytope of Type {36,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,10,2}*1440
if this polytope has a name.
Group : SmallGroup(1440,1583)
Rank : 4
Schlafli Type : {36,10,2}
Number of vertices, edges, etc : 36, 180, 10, 2
Order of s₀s₁s₂s₃ : 180
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
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 : {18,10,2}*720
   3-fold quotients : {12,10,2}*480
   5-fold quotients : {36,2,2}*288
   6-fold quotients : {6,10,2}*240
   9-fold quotients : {4,10,2}*160
   10-fold quotients : {18,2,2}*144
   15-fold quotients : {12,2,2}*96
   18-fold quotients : {2,10,2}*80
   20-fold quotients : {9,2,2}*72
   30-fold quotients : {6,2,2}*48
   36-fold quotients : {2,5,2}*40
   45-fold quotients : {4,2,2}*32
   60-fold quotients : {3,2,2}*24
   90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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);;
s3 := (181,182);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
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(182)!(  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(182)!(  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(182)!(  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);
s3 := Sym(182)!(181,182);
poly := sub<Sym(182)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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 >;

to this polytope