Polytope of Type {14,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,4}*1792c
if this polytope has a name.
Group : SmallGroup(1792,1083553)
Rank : 3
Schlafli Type : {14,4}
Number of vertices, edges, etc : 224, 448, 64
Order of s₀s₁s₂ : 14
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {7,4}*896
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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)( 21, 99)( 22,100)
( 23,115)( 24,116)( 25, 35)( 26, 36)( 27, 51)( 28, 52)( 29, 67)( 30, 68)
( 31, 83)( 32, 84)( 37,105)( 38,106)( 39,121)( 40,122)( 43, 57)( 44, 58)
( 45, 73)( 46, 74)( 47, 89)( 48, 90)( 53,107)( 54,108)( 55,123)( 56,124)
( 61, 75)( 62, 76)( 63, 91)( 64, 92)( 69,109)( 70,110)( 71,125)( 72,126)
( 79, 93)( 80, 94)( 85,111)( 86,112)( 87,127)( 88,128)(103,117)(104,118);;
s1 := (  1,  2)(  3, 34)(  4, 33)(  5,114)(  6,113)(  7, 82)(  8, 81)(  9, 66)
( 10, 65)( 11, 98)( 12, 97)( 13, 50)( 14, 49)( 15, 18)( 16, 17)( 19, 48)
( 20, 47)( 21,128)( 22,127)( 23, 96)( 24, 95)( 25, 80)( 26, 79)( 27,112)
( 28,111)( 29, 64)( 30, 63)( 31, 32)( 35, 36)( 37,116)( 38,115)( 39, 84)
( 40, 83)( 41, 68)( 42, 67)( 43,100)( 44, 99)( 45, 52)( 46, 51)( 53,126)
( 54,125)( 55, 94)( 56, 93)( 57, 78)( 58, 77)( 59,110)( 60,109)( 61, 62)
( 69,122)( 70,121)( 71, 90)( 72, 89)( 73, 74)( 75,106)( 76,105)( 85,120)
( 86,119)( 87, 88)( 91,104)( 92,103)(101,124)(102,123)(107,108)(117,118);;
s2 := (  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);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2 ];;
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)( 21, 99)
( 22,100)( 23,115)( 24,116)( 25, 35)( 26, 36)( 27, 51)( 28, 52)( 29, 67)
( 30, 68)( 31, 83)( 32, 84)( 37,105)( 38,106)( 39,121)( 40,122)( 43, 57)
( 44, 58)( 45, 73)( 46, 74)( 47, 89)( 48, 90)( 53,107)( 54,108)( 55,123)
( 56,124)( 61, 75)( 62, 76)( 63, 91)( 64, 92)( 69,109)( 70,110)( 71,125)
( 72,126)( 79, 93)( 80, 94)( 85,111)( 86,112)( 87,127)( 88,128)(103,117)
(104,118);
s1 := Sym(128)!(  1,  2)(  3, 34)(  4, 33)(  5,114)(  6,113)(  7, 82)(  8, 81)
(  9, 66)( 10, 65)( 11, 98)( 12, 97)( 13, 50)( 14, 49)( 15, 18)( 16, 17)
( 19, 48)( 20, 47)( 21,128)( 22,127)( 23, 96)( 24, 95)( 25, 80)( 26, 79)
( 27,112)( 28,111)( 29, 64)( 30, 63)( 31, 32)( 35, 36)( 37,116)( 38,115)
( 39, 84)( 40, 83)( 41, 68)( 42, 67)( 43,100)( 44, 99)( 45, 52)( 46, 51)
( 53,126)( 54,125)( 55, 94)( 56, 93)( 57, 78)( 58, 77)( 59,110)( 60,109)
( 61, 62)( 69,122)( 70,121)( 71, 90)( 72, 89)( 73, 74)( 75,106)( 76,105)
( 85,120)( 86,119)( 87, 88)( 91,104)( 92,103)(101,124)(102,123)(107,108)
(117,118);
s2 := 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);
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, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s2 >;

References : None.
to this polytope