Polytope of Type {20,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,8}*1280h
if this polytope has a name.
Group : SmallGroup(1280,1116393)
Rank : 3
Schlafli Type : {20,8}
Number of vertices, edges, etc : 80, 320, 32
Order of s₀s₁s₂ : 5
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
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 : {10,8}*640d, {20,4}*640e
   4-fold quotients : {5,8}*320a, {10,4}*320b
   8-fold quotients : {5,4}*160
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  5,  6)(  7,  8)(  9, 10)( 11, 12)( 17, 27)( 18, 28)( 19, 25)( 20, 26)
( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 33, 41)( 34, 42)( 35, 43)( 36, 44)
( 37, 46)( 38, 45)( 39, 48)( 40, 47)( 49, 51)( 50, 52)( 53, 56)( 54, 55)
( 57, 60)( 58, 59)( 61, 63)( 62, 64)( 65,121)( 66,122)( 67,123)( 68,124)
( 69,126)( 70,125)( 71,128)( 72,127)( 73,113)( 74,114)( 75,115)( 76,116)
( 77,118)( 78,117)( 79,120)( 80,119)( 81, 98)( 82, 97)( 83,100)( 84, 99)
( 85,101)( 86,102)( 87,103)( 88,104)( 89,105)( 90,106)( 91,107)( 92,108)
( 93,110)( 94,109)( 95,112)( 96,111);;
s1 := (  1,  6)(  2,  5)(  3,  8)(  4,  7)(  9,102)( 10,101)( 11,104)( 12,103)
( 13, 98)( 14, 97)( 15,100)( 16, 99)( 17, 61)( 18, 62)( 19, 63)( 20, 64)
( 21, 57)( 22, 58)( 23, 59)( 24, 60)( 25, 96)( 26, 95)( 27, 94)( 28, 93)
( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 78)( 34, 77)( 35, 80)( 36, 79)
( 37, 74)( 38, 73)( 39, 76)( 40, 75)( 41, 48)( 42, 47)( 43, 46)( 44, 45)
( 49,118)( 50,117)( 51,120)( 52,119)( 53,114)( 54,113)( 55,116)( 56,115)
( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 81,126)( 82,125)( 83,128)( 84,127)
( 85,122)( 86,121)( 87,124)( 88,123)(105,111)(106,112)(107,109)(108,110);;
s2 := (  1, 16)(  2, 15)(  3, 14)(  4, 13)(  5, 11)(  6, 12)(  7,  9)(  8, 10)
( 17, 32)( 18, 31)( 19, 30)( 20, 29)( 21, 27)( 22, 28)( 23, 25)( 24, 26)
( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 43)( 38, 44)( 39, 41)( 40, 42)
( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 59)( 54, 60)( 55, 57)( 56, 58)
( 65, 80)( 66, 79)( 67, 78)( 68, 77)( 69, 75)( 70, 76)( 71, 73)( 72, 74)
( 81, 96)( 82, 95)( 83, 94)( 84, 93)( 85, 91)( 86, 92)( 87, 89)( 88, 90)
( 97,112)( 98,111)( 99,110)(100,109)(101,107)(102,108)(103,105)(104,106)
(113,128)(114,127)(115,126)(116,125)(117,123)(118,124)(119,121)(120,122);;
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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope