Polytope of Type {10,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8}*1280b
if this polytope has a name.
Group : SmallGroup(1280,1116393)
Rank : 3
Schlafli Type : {10,8}
Number of vertices, edges, etc : 80, 320, 64
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {5,8}*640b, {10,4}*640a
   4-fold quotients : {5,4}*320
   8-fold quotients : {5,4}*160
   64-fold quotients : {5,2}*20
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,  4)(  2,  3)(  5,  7)(  6,  8)(  9,123)( 10,124)( 11,121)( 12,122)
( 13,128)( 14,127)( 15,126)( 16,125)( 21, 22)( 23, 24)( 25,107)( 26,108)
( 27,105)( 28,106)( 29,112)( 30,111)( 31,110)( 32,109)( 33, 52)( 34, 51)
( 35, 50)( 36, 49)( 37, 55)( 38, 56)( 39, 53)( 40, 54)( 41, 74)( 42, 73)
( 43, 76)( 44, 75)( 45, 77)( 46, 78)( 47, 79)( 48, 80)( 57, 91)( 58, 92)
( 59, 89)( 60, 90)( 61, 96)( 62, 95)( 63, 94)( 64, 93)( 65, 83)( 66, 84)
( 67, 81)( 68, 82)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 97, 99)( 98,100)
(101,104)(102,103)(113,114)(115,116);;
s2 := (  1, 13)(  2, 14)(  3, 15)(  4, 16)(  5, 10)(  6,  9)(  7, 12)(  8, 11)
( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 26)( 22, 25)( 23, 28)( 24, 27)
( 33, 45)( 34, 46)( 35, 47)( 36, 48)( 37, 42)( 38, 41)( 39, 44)( 40, 43)
( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 58)( 54, 57)( 55, 60)( 56, 59)
( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 74)( 70, 73)( 71, 76)( 72, 75)
( 81, 93)( 82, 94)( 83, 95)( 84, 96)( 85, 90)( 86, 89)( 87, 92)( 88, 91)
( 97,109)( 98,110)( 99,111)(100,112)(101,106)(102,105)(103,108)(104,107)
(113,125)(114,126)(115,127)(116,128)(117,122)(118,121)(119,124)(120,123);;
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*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, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*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*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,  4)(  2,  3)(  5,  7)(  6,  8)(  9,123)( 10,124)( 11,121)
( 12,122)( 13,128)( 14,127)( 15,126)( 16,125)( 21, 22)( 23, 24)( 25,107)
( 26,108)( 27,105)( 28,106)( 29,112)( 30,111)( 31,110)( 32,109)( 33, 52)
( 34, 51)( 35, 50)( 36, 49)( 37, 55)( 38, 56)( 39, 53)( 40, 54)( 41, 74)
( 42, 73)( 43, 76)( 44, 75)( 45, 77)( 46, 78)( 47, 79)( 48, 80)( 57, 91)
( 58, 92)( 59, 89)( 60, 90)( 61, 96)( 62, 95)( 63, 94)( 64, 93)( 65, 83)
( 66, 84)( 67, 81)( 68, 82)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 97, 99)
( 98,100)(101,104)(102,103)(113,114)(115,116);
s2 := Sym(128)!(  1, 13)(  2, 14)(  3, 15)(  4, 16)(  5, 10)(  6,  9)(  7, 12)
(  8, 11)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 26)( 22, 25)( 23, 28)
( 24, 27)( 33, 45)( 34, 46)( 35, 47)( 36, 48)( 37, 42)( 38, 41)( 39, 44)
( 40, 43)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 58)( 54, 57)( 55, 60)
( 56, 59)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 74)( 70, 73)( 71, 76)
( 72, 75)( 81, 93)( 82, 94)( 83, 95)( 84, 96)( 85, 90)( 86, 89)( 87, 92)
( 88, 91)( 97,109)( 98,110)( 99,111)(100,112)(101,106)(102,105)(103,108)
(104,107)(113,125)(114,126)(115,127)(116,128)(117,122)(118,121)(119,124)
(120,123);
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*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, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
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