Polytope of Type {20,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,8}*1280b
if this polytope has a name.
Group : SmallGroup(1280,90281)
Rank : 3
Schlafli Type : {20,8}
Number of vertices, edges, etc : 80, 320, 32
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,8}*640b
   4-fold quotients : {20,4}*320
   5-fold quotients : {4,8}*256b
   8-fold quotients : {20,4}*160
   10-fold quotients : {4,8}*128b
   16-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {4,4}*64
   32-fold quotients : {10,2}*40
   40-fold quotients : {4,4}*32
   64-fold quotients : {5,2}*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 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 11, 16)( 12, 20)( 13, 19)( 14, 18)
( 15, 17)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 31, 36)( 32, 40)( 33, 39)
( 34, 38)( 35, 37)( 41, 76)( 42, 80)( 43, 79)( 44, 78)( 45, 77)( 46, 71)
( 47, 75)( 48, 74)( 49, 73)( 50, 72)( 51, 61)( 52, 65)( 53, 64)( 54, 63)
( 55, 62)( 56, 66)( 57, 70)( 58, 69)( 59, 68)( 60, 67)( 82, 85)( 83, 84)
( 87, 90)( 88, 89)( 91, 96)( 92,100)( 93, 99)( 94, 98)( 95, 97)(102,105)
(103,104)(107,110)(108,109)(111,116)(112,120)(113,119)(114,118)(115,117)
(121,156)(122,160)(123,159)(124,158)(125,157)(126,151)(127,155)(128,154)
(129,153)(130,152)(131,141)(132,145)(133,144)(134,143)(135,142)(136,146)
(137,150)(138,149)(139,148)(140,147);;
s1 := (  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 13)( 14, 15)( 16, 18)( 19, 20)
( 21, 33)( 22, 32)( 23, 31)( 24, 35)( 25, 34)( 26, 38)( 27, 37)( 28, 36)
( 29, 40)( 30, 39)( 41, 43)( 44, 45)( 46, 48)( 49, 50)( 51, 53)( 54, 55)
( 56, 58)( 59, 60)( 61, 73)( 62, 72)( 63, 71)( 64, 75)( 65, 74)( 66, 78)
( 67, 77)( 68, 76)( 69, 80)( 70, 79)( 81,123)( 82,122)( 83,121)( 84,125)
( 85,124)( 86,128)( 87,127)( 88,126)( 89,130)( 90,129)( 91,133)( 92,132)
( 93,131)( 94,135)( 95,134)( 96,138)( 97,137)( 98,136)( 99,140)(100,139)
(101,153)(102,152)(103,151)(104,155)(105,154)(106,158)(107,157)(108,156)
(109,160)(110,159)(111,143)(112,142)(113,141)(114,145)(115,144)(116,148)
(117,147)(118,146)(119,150)(120,149);;
s2 := (  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);;
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*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope