Polytope of Type {4,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,14}*1792a
if this polytope has a name.
Group : SmallGroup(1792,1083551)
Rank : 3
Schlafli Type : {4,14}
Number of vertices, edges, etc : 64, 448, 224
Order of s₀s₁s₂ : 14
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
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, 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,  2)(  3, 66)(  4, 65)(  5, 82)(  6, 81)(  7, 18)(  8, 17)(  9, 50)
( 10, 49)( 11,114)( 12,113)( 13, 98)( 14, 97)( 15, 34)( 16, 33)( 19, 71)
( 20, 72)( 21, 87)( 22, 88)( 23, 24)( 25, 55)( 26, 56)( 27,120)( 28,119)
( 29,104)( 30,103)( 31, 39)( 32, 40)( 35, 79)( 36, 80)( 37, 96)( 38, 95)
( 41, 64)( 42, 63)( 43,127)( 44,128)( 45,112)( 46,111)( 51, 74)( 52, 73)
( 53, 89)( 54, 90)( 59,121)( 60,122)( 61,106)( 62,105)( 67, 68)( 69, 83)
( 70, 84)( 75,116)( 76,115)( 77, 99)( 78,100)( 85, 86)( 91,118)( 92,117)
( 93,101)( 94,102)(107,125)(108,126);;
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, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2 ];;
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, 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,  2)(  3, 66)(  4, 65)(  5, 82)(  6, 81)(  7, 18)(  8, 17)
(  9, 50)( 10, 49)( 11,114)( 12,113)( 13, 98)( 14, 97)( 15, 34)( 16, 33)
( 19, 71)( 20, 72)( 21, 87)( 22, 88)( 23, 24)( 25, 55)( 26, 56)( 27,120)
( 28,119)( 29,104)( 30,103)( 31, 39)( 32, 40)( 35, 79)( 36, 80)( 37, 96)
( 38, 95)( 41, 64)( 42, 63)( 43,127)( 44,128)( 45,112)( 46,111)( 51, 74)
( 52, 73)( 53, 89)( 54, 90)( 59,121)( 60,122)( 61,106)( 62,105)( 67, 68)
( 69, 83)( 70, 84)( 75,116)( 76,115)( 77, 99)( 78,100)( 85, 86)( 91,118)
( 92,117)( 93,101)( 94,102)(107,125)(108,126);
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, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2 >;

References : None.
to this polytope