Polytope of Type {2,160}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,160}*640
if this polytope has a name.
Group : SmallGroup(640,2242)
Rank : 3
Schlafli Type : {2,160}
Number of vertices, edges, etc : 2, 160, 160
Order of s₀s₁s₂ : 160
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,160,2} of size 1280
Vertex Figure Of :
   {2,2,160} of size 1280
   {3,2,160} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,80}*320
   4-fold quotients : {2,40}*160
   5-fold quotients : {2,32}*128
   8-fold quotients : {2,20}*80
   10-fold quotients : {2,16}*64
   16-fold quotients : {2,10}*40
   20-fold quotients : {2,8}*32
   32-fold quotients : {2,5}*20
   40-fold quotients : {2,4}*16
   80-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,160}*1280a, {2,320}*1280
   3-fold covers : {2,480}*1920, {6,160}*1920
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

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

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