Polytope of Type {10,20}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,20}*1280b
if this polytope has a name.
Group : SmallGroup(1280,1116393)
Rank : 3
Schlafli Type : {10,20}
Number of vertices, edges, etc : 32, 320, 64
Order of s0s1s2 : 8
Order of s0s1s2s1 : 20
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}*640a, {5,20}*640b
   4-fold quotients : {10,5}*320a, {5,10}*320b
   8-fold quotients : {5,5}*160
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

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, 75)(  2, 76)(  3, 73)(  4, 74)(  5, 80)(  6, 79)(  7, 78)(  8, 77)(  9, 12)( 10, 11)( 13, 15)( 14, 16)( 21, 22)( 23, 24)( 25, 82)( 26, 81)( 27, 84)( 28, 83)( 29, 85)( 30, 86)( 31, 87)( 32, 88)( 33, 57)( 34, 58)( 35, 59)( 36, 60)( 37, 62)( 38, 61)( 39, 64)( 40, 63)( 41,122)( 42,121)( 43,124)( 44,123)( 45,125)( 46,126)( 47,127)( 48,128)( 49, 98)( 50, 97)( 51,100)( 52, 99)( 53,101)( 54,102)( 55,103)( 56,104)( 65, 66)( 67, 68)( 89, 91)( 90, 92)( 93, 96)( 94, 95)(105,115)(106,116)(107,113)(108,114)(109,120)(110,119)(111,118)(112,117);;
s2 := (  1, 15)(  2, 16)(  3, 13)(  4, 14)(  5, 11)(  6, 12)(  7,  9)(  8, 10)( 17, 22)( 18, 21)( 19, 24)( 20, 23)( 25, 29)( 26, 30)( 27, 31)( 28, 32)( 33, 40)( 34, 39)( 35, 38)( 36, 37)( 41, 47)( 42, 48)( 43, 45)( 44, 46)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65,120)( 66,119)( 67,118)( 68,117)( 69,116)( 70,115)( 71,114)( 72,113)( 73,127)( 74,128)( 75,125)( 76,126)( 77,123)( 78,124)( 79,121)( 80,122)( 81,112)( 82,111)( 83,110)( 84,109)( 85,108)( 86,107)( 87,106)( 88,105)( 89,104)( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97);;
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*s2*s1*s2*s0*s1*s2*s0*s1*s2*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*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*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, 75)(  2, 76)(  3, 73)(  4, 74)(  5, 80)(  6, 79)(  7, 78)(  8, 77)(  9, 12)( 10, 11)( 13, 15)( 14, 16)( 21, 22)( 23, 24)( 25, 82)( 26, 81)( 27, 84)( 28, 83)( 29, 85)( 30, 86)( 31, 87)( 32, 88)( 33, 57)( 34, 58)( 35, 59)( 36, 60)( 37, 62)( 38, 61)( 39, 64)( 40, 63)( 41,122)( 42,121)( 43,124)( 44,123)( 45,125)( 46,126)( 47,127)( 48,128)( 49, 98)( 50, 97)( 51,100)( 52, 99)( 53,101)( 54,102)( 55,103)( 56,104)( 65, 66)( 67, 68)( 89, 91)( 90, 92)( 93, 96)( 94, 95)(105,115)(106,116)(107,113)(108,114)(109,120)(110,119)(111,118)(112,117);
s2 := Sym(128)!(  1, 15)(  2, 16)(  3, 13)(  4, 14)(  5, 11)(  6, 12)(  7,  9)(  8, 10)( 17, 22)( 18, 21)( 19, 24)( 20, 23)( 25, 29)( 26, 30)( 27, 31)( 28, 32)( 33, 40)( 34, 39)( 35, 38)( 36, 37)( 41, 47)( 42, 48)( 43, 45)( 44, 46)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65,120)( 66,119)( 67,118)( 68,117)( 69,116)( 70,115)( 71,114)( 72,113)( 73,127)( 74,128)( 75,125)( 76,126)( 77,123)( 78,124)( 79,121)( 80,122)( 81,112)( 82,111)( 83,110)( 84,109)( 85,108)( 86,107)( 87,106)( 88,105)( 89,104)( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97);
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*s2*s1*s2*s0*s1*s2*s0*s1*s2*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*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1 >;
References : None.
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