Polytope of Type {20,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,10}*1280f
if this polytope has a name.
Group : SmallGroup(1280,1116459)
Rank : 3
Schlafli Type : {20,10}
Number of vertices, edges, etc : 64, 320, 32
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 10
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 : {10,10}*640d
   4-fold quotients : {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 := (  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9, 13)( 10, 14)( 11, 16)( 12, 15)
( 17, 30)( 18, 29)( 19, 31)( 20, 32)( 21, 26)( 22, 25)( 23, 27)( 24, 28)
( 33, 45)( 34, 46)( 35, 48)( 36, 47)( 37, 41)( 38, 42)( 39, 44)( 40, 43)
( 49, 54)( 50, 53)( 51, 55)( 52, 56)( 57, 62)( 58, 61)( 59, 63)( 60, 64)
( 65,125)( 66,126)( 67,128)( 68,127)( 69,121)( 70,122)( 71,124)( 72,123)
( 73,117)( 74,118)( 75,120)( 76,119)( 77,113)( 78,114)( 79,116)( 80,115)
( 81,101)( 82,102)( 83,104)( 84,103)( 85, 97)( 86, 98)( 87,100)( 88, 99)
( 89,109)( 90,110)( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107);;
s1 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9,100)( 10, 99)( 11, 98)( 12, 97)
( 13,104)( 14,103)( 15,102)( 16,101)( 17, 60)( 18, 59)( 19, 58)( 20, 57)
( 21, 64)( 22, 63)( 23, 62)( 24, 61)( 25, 92)( 26, 91)( 27, 90)( 28, 89)
( 29, 96)( 30, 95)( 31, 94)( 32, 93)( 33, 76)( 34, 75)( 35, 74)( 36, 73)
( 37, 80)( 38, 79)( 39, 78)( 40, 77)( 41, 44)( 42, 43)( 45, 48)( 46, 47)
( 49,115)( 50,116)( 51,113)( 52,114)( 53,119)( 54,120)( 55,117)( 56,118)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 81,124)( 82,123)( 83,122)( 84,121)
( 85,128)( 86,127)( 87,126)( 88,125)(105,108)(106,107)(109,112)(110,111);;
s2 := (  1, 10)(  2,  9)(  3, 12)(  4, 11)(  5, 14)(  6, 13)(  7, 16)(  8, 15)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65,114)( 66,113)( 67,116)( 68,115)( 69,118)( 70,117)( 71,120)( 72,119)
( 73,122)( 74,121)( 75,124)( 76,123)( 77,126)( 78,125)( 79,128)( 80,127)
( 81,106)( 82,105)( 83,108)( 84,107)( 85,110)( 86,109)( 87,112)( 88,111)
( 89, 98)( 90, 97)( 91,100)( 92, 99)( 93,102)( 94,101)( 95,104)( 96,103);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
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