Polytope of Type {8,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,20}*1280b
if this polytope has a name.
Group : SmallGroup(1280,90281)
Rank : 3
Schlafli Type : {8,20}
Number of vertices, edges, etc : 32, 320, 80
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {8,20}*640b
   4-fold quotients : {4,20}*320
   5-fold quotients : {8,4}*256b
   8-fold quotients : {4,20}*160
   10-fold quotients : {8,4}*128b
   16-fold quotients : {2,20}*80, {4,10}*80
   20-fold quotients : {4,4}*64
   32-fold quotients : {2,10}*40
   40-fold quotients : {4,4}*32
   64-fold quotients : {2,5}*20
   80-fold quotients : {2,4}*16, {4,2}*16
   160-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

References : None.
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