Polytope of Type {8,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,7}*1792a
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 : 8
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, 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);;
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, 
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
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, 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);
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, 
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
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