Polytope of Type {7,7}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,7}*1792a
if this polytope has a name.
Group : SmallGroup(1792,1083551)
Rank : 3
Schlafli Type : {7,7}
Number of vertices, edges, etc : 128, 448, 128
Order of s0s1s2 : 8
Order of s0s1s2s1 : 14
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 : {7,7}*896
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s2*s1*s2*s1*s0*s2*s1*s2*s1> of order 2.
      64 facets:
         64 of {7}*14
      64 vertex figures:
         64 of {7}*14
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1> of order 2.
      64 facets:
         64 of {7}*14
      64 vertex figures:
         64 of {7}*14
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1> of order 4.
      32 facets:
         32 of {7}*14
      32 vertex figures:
         32 of {7}*14
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1> of order 4.
      32 facets:
         32 of {7}*14
      32 vertex figures:
         32 of {7}*14
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1> of order 8.
      16 facets:
         16 of {7}*14
      16 vertex figures:
         16 of {7}*14

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