Polytope of Type {20,5}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,5}*1280
if this polytope has a name.
Group : SmallGroup(1280,1116393)
Rank : 3
Schlafli Type : {20,5}
Number of vertices, edges, etc : 128, 320, 32
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 : {10,5}*640, {20,5}*640a, {20,5}*640b
   4-fold quotients : {5,5}*320, {10,5}*320a, {10,5}*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,  6)(  2,  5)(  3,  8)(  4,  7)(  9,102)( 10,101)( 11,104)( 12,103)( 13, 98)( 14, 97)( 15,100)( 16, 99)( 17, 61)( 18, 62)( 19, 63)( 20, 64)( 21, 57)( 22, 58)( 23, 59)( 24, 60)( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 78)( 34, 77)( 35, 80)( 36, 79)( 37, 74)( 38, 73)( 39, 76)( 40, 75)( 41, 48)( 42, 47)( 43, 46)( 44, 45)( 49,118)( 50,117)( 51,120)( 52,119)( 53,114)( 54,113)( 55,116)( 56,115)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 81,126)( 82,125)( 83,128)( 84,127)( 85,122)( 86,121)( 87,124)( 88,123)(105,111)(106,112)(107,109)(108,110);;
s2 := (  1, 16)(  2, 15)(  3, 14)(  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 25, 30)( 26, 29)( 27, 32)( 28, 31)( 33, 39)( 34, 40)( 35, 37)( 36, 38)( 41, 48)( 42, 47)( 43, 46)( 44, 45)( 49, 62)( 50, 61)( 51, 64)( 52, 63)( 53, 58)( 54, 57)( 55, 60)( 56, 59)( 65,119)( 66,120)( 67,117)( 68,118)( 69,115)( 70,116)( 71,113)( 72,114)( 73,128)( 74,127)( 75,126)( 76,125)( 77,124)( 78,123)( 79,122)( 80,121)( 81,111)( 82,112)( 83,109)( 84,110)( 85,107)( 86,108)( 87,105)( 88,106)( 89,103)( 90,104)( 91,101)( 92,102)( 93, 99)( 94,100)( 95, 97)( 96, 98);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*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,  6)(  2,  5)(  3,  8)(  4,  7)(  9,102)( 10,101)( 11,104)( 12,103)( 13, 98)( 14, 97)( 15,100)( 16, 99)( 17, 61)( 18, 62)( 19, 63)( 20, 64)( 21, 57)( 22, 58)( 23, 59)( 24, 60)( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 78)( 34, 77)( 35, 80)( 36, 79)( 37, 74)( 38, 73)( 39, 76)( 40, 75)( 41, 48)( 42, 47)( 43, 46)( 44, 45)( 49,118)( 50,117)( 51,120)( 52,119)( 53,114)( 54,113)( 55,116)( 56,115)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 81,126)( 82,125)( 83,128)( 84,127)( 85,122)( 86,121)( 87,124)( 88,123)(105,111)(106,112)(107,109)(108,110);
s2 := Sym(128)!(  1, 16)(  2, 15)(  3, 14)(  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 25, 30)( 26, 29)( 27, 32)( 28, 31)( 33, 39)( 34, 40)( 35, 37)( 36, 38)( 41, 48)( 42, 47)( 43, 46)( 44, 45)( 49, 62)( 50, 61)( 51, 64)( 52, 63)( 53, 58)( 54, 57)( 55, 60)( 56, 59)( 65,119)( 66,120)( 67,117)( 68,118)( 69,115)( 70,116)( 71,113)( 72,114)( 73,128)( 74,127)( 75,126)( 76,125)( 77,124)( 78,123)( 79,122)( 80,121)( 81,111)( 82,112)( 83,109)( 84,110)( 85,107)( 86,108)( 87,105)( 88,106)( 89,103)( 90,104)( 91,101)( 92,102)( 93, 99)( 94,100)( 95, 97)( 96, 98);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1 >;
References : None.
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