Polytope of Type {8,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,7}*1792c
if this polytope has a name.
Group : SmallGroup(1792,1083551)
Rank : 3
Schlafli Type : {8,7}
Number of vertices, edges, etc : 128, 448, 112
Order of s₀s₁s₂ : 14
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {4,7}*896
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope