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Polytope of Type {8,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,10}*1280f
if this polytope has a name.
Group : SmallGroup(1280,1116459)
Rank : 3
Schlafli Type : {8,10}
Number of vertices, edges, etc : 64, 320, 80
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 : {4,10}*640b
   4-fold quotients : {4,5}*320, {4,10}*320a, {4,10}*320b
   8-fold quotients : {4,5}*160
   32-fold quotients : {2,10}*40
   64-fold quotients : {2,5}*20
   160-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,101)(  2,102)(  3,104)(  4,103)(  5, 97)(  6, 98)(  7,100)(  8, 99)
(  9,110)( 10,109)( 11,111)( 12,112)( 13,106)( 14,105)( 15,107)( 16,108)
( 17,117)( 18,118)( 19,120)( 20,119)( 21,113)( 22,114)( 23,116)( 24,115)
( 25,126)( 26,125)( 27,127)( 28,128)( 29,122)( 30,121)( 31,123)( 32,124)
( 33, 69)( 34, 70)( 35, 72)( 36, 71)( 37, 65)( 38, 66)( 39, 68)( 40, 67)
( 41, 78)( 42, 77)( 43, 79)( 44, 80)( 45, 74)( 46, 73)( 47, 75)( 48, 76)
( 49, 85)( 50, 86)( 51, 88)( 52, 87)( 53, 81)( 54, 82)( 55, 84)( 56, 83)
( 57, 94)( 58, 93)( 59, 95)( 60, 96)( 61, 90)( 62, 89)( 63, 91)( 64, 92);;
s1 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 32)( 22, 31)( 23, 30)( 24, 29)
( 33, 43)( 34, 44)( 35, 41)( 36, 42)( 37, 47)( 38, 48)( 39, 45)( 40, 46)
( 49, 52)( 50, 51)( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)( 62, 63)
( 65,123)( 66,124)( 67,121)( 68,122)( 69,127)( 70,128)( 71,125)( 72,126)
( 73,115)( 74,116)( 75,113)( 76,114)( 77,119)( 78,120)( 79,117)( 80,118)
( 81, 99)( 82,100)( 83, 97)( 84, 98)( 85,103)( 86,104)( 87,101)( 88,102)
( 89,107)( 90,108)( 91,105)( 92,106)( 93,111)( 94,112)( 95,109)( 96,110);;
s2 := (  9,121)( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)( 16,128)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25,105)( 26,106)( 27,107)( 28,108)
( 29,109)( 30,110)( 31,111)( 32,112)( 33, 50)( 34, 49)( 35, 52)( 36, 51)
( 37, 54)( 38, 53)( 39, 56)( 40, 55)( 41, 73)( 42, 74)( 43, 75)( 44, 76)
( 45, 77)( 46, 78)( 47, 79)( 48, 80)( 57, 90)( 58, 89)( 59, 92)( 60, 91)
( 61, 94)( 62, 93)( 63, 96)( 64, 95)( 65, 82)( 66, 81)( 67, 84)( 68, 83)
( 69, 86)( 70, 85)( 71, 88)( 72, 87)(113,114)(115,116)(117,118)(119,120);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(128)!(  1,101)(  2,102)(  3,104)(  4,103)(  5, 97)(  6, 98)(  7,100)
(  8, 99)(  9,110)( 10,109)( 11,111)( 12,112)( 13,106)( 14,105)( 15,107)
( 16,108)( 17,117)( 18,118)( 19,120)( 20,119)( 21,113)( 22,114)( 23,116)
( 24,115)( 25,126)( 26,125)( 27,127)( 28,128)( 29,122)( 30,121)( 31,123)
( 32,124)( 33, 69)( 34, 70)( 35, 72)( 36, 71)( 37, 65)( 38, 66)( 39, 68)
( 40, 67)( 41, 78)( 42, 77)( 43, 79)( 44, 80)( 45, 74)( 46, 73)( 47, 75)
( 48, 76)( 49, 85)( 50, 86)( 51, 88)( 52, 87)( 53, 81)( 54, 82)( 55, 84)
( 56, 83)( 57, 94)( 58, 93)( 59, 95)( 60, 96)( 61, 90)( 62, 89)( 63, 91)
( 64, 92);
s1 := Sym(128)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 32)( 22, 31)( 23, 30)
( 24, 29)( 33, 43)( 34, 44)( 35, 41)( 36, 42)( 37, 47)( 38, 48)( 39, 45)
( 40, 46)( 49, 52)( 50, 51)( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)
( 62, 63)( 65,123)( 66,124)( 67,121)( 68,122)( 69,127)( 70,128)( 71,125)
( 72,126)( 73,115)( 74,116)( 75,113)( 76,114)( 77,119)( 78,120)( 79,117)
( 80,118)( 81, 99)( 82,100)( 83, 97)( 84, 98)( 85,103)( 86,104)( 87,101)
( 88,102)( 89,107)( 90,108)( 91,105)( 92,106)( 93,111)( 94,112)( 95,109)
( 96,110);
s2 := Sym(128)!(  9,121)( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)
( 16,128)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25,105)( 26,106)( 27,107)
( 28,108)( 29,109)( 30,110)( 31,111)( 32,112)( 33, 50)( 34, 49)( 35, 52)
( 36, 51)( 37, 54)( 38, 53)( 39, 56)( 40, 55)( 41, 73)( 42, 74)( 43, 75)
( 44, 76)( 45, 77)( 46, 78)( 47, 79)( 48, 80)( 57, 90)( 58, 89)( 59, 92)
( 60, 91)( 61, 94)( 62, 93)( 63, 96)( 64, 95)( 65, 82)( 66, 81)( 67, 84)
( 68, 83)( 69, 86)( 70, 85)( 71, 88)( 72, 87)(113,114)(115,116)(117,118)
(119,120);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1 >; 
 
References : None.
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