Polytope of Type {160,2}

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

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

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