Polytope of Type {10,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10}*1280a
if this polytope has a name.
Group : SmallGroup(1280,1116450)
Rank : 3
Schlafli Type : {10,10}
Number of vertices, edges, etc : 64, 320, 64
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
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 : {5,10}*640, {10,5}*640, {10,10}*640a, {10,10}*640b, {10,10}*640c, {10,10}*640d
   4-fold quotients : {5,5}*320, {5,10}*320a, {10,5}*320a, {5,10}*320b, {10,5}*320b
   8-fold quotients : {5,5}*160
   160-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

References : None.
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