Polytope of Type {4,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,14}*1792c
if this polytope has a name.
Group : SmallGroup(1792,1083553)
Rank : 3
Schlafli Type : {4,14}
Number of vertices, edges, etc : 64, 448, 224
Order of s₀s₁s₂ : 14
Order of s₀s₁s₂s₁ : 4
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, 19)(  2, 20)(  3, 17)(  4, 18)(  5, 23)(  6, 24)(  7, 21)(  8, 22)
(  9, 27)( 10, 28)( 11, 25)( 12, 26)( 13, 31)( 14, 32)( 15, 29)( 16, 30)
( 33, 51)( 34, 52)( 35, 49)( 36, 50)( 37, 55)( 38, 56)( 39, 53)( 40, 54)
( 41, 59)( 42, 60)( 43, 57)( 44, 58)( 45, 63)( 46, 64)( 47, 61)( 48, 62)
( 65, 83)( 66, 84)( 67, 81)( 68, 82)( 69, 87)( 70, 88)( 71, 85)( 72, 86)
( 73, 91)( 74, 92)( 75, 89)( 76, 90)( 77, 95)( 78, 96)( 79, 93)( 80, 94)
( 97,115)( 98,116)( 99,113)(100,114)(101,119)(102,120)(103,117)(104,118)
(105,123)(106,124)(107,121)(108,122)(109,127)(110,128)(111,125)(112,126);;
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, 47)( 20, 48)
( 21,127)( 22,128)( 23, 95)( 24, 96)( 25, 79)( 26, 80)( 27,111)( 28,112)
( 29, 63)( 30, 64)( 37,115)( 38,116)( 39, 83)( 40, 84)( 41, 67)( 42, 68)
( 43, 99)( 44,100)( 45, 51)( 46, 52)( 53,125)( 54,126)( 55, 93)( 56, 94)
( 57, 77)( 58, 78)( 59,109)( 60,110)( 69,121)( 70,122)( 71, 89)( 72, 90)
( 75,105)( 76,106)( 85,119)( 86,120)( 91,103)( 92,104)(101,123)(102,124);;
s2 := (  1,  2)(  3, 18)(  4, 17)(  5, 98)(  6, 97)(  7,114)(  8,113)(  9, 34)
( 10, 33)( 11, 50)( 12, 49)( 13, 66)( 14, 65)( 15, 82)( 16, 81)( 19, 20)
( 21,100)( 22, 99)( 23,116)( 24,115)( 25, 36)( 26, 35)( 27, 52)( 28, 51)
( 29, 68)( 30, 67)( 31, 84)( 32, 83)( 37,106)( 38,105)( 39,122)( 40,121)
( 41, 42)( 43, 58)( 44, 57)( 45, 74)( 46, 73)( 47, 90)( 48, 89)( 53,108)
( 54,107)( 55,124)( 56,123)( 59, 60)( 61, 76)( 62, 75)( 63, 92)( 64, 91)
( 69,110)( 70,109)( 71,126)( 72,125)( 77, 78)( 79, 94)( 80, 93)( 85,112)
( 86,111)( 87,128)( 88,127)( 95, 96)(101,102)(103,118)(104,117)(119,120);;
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope