Polytope of Type {7,4}

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

References : None.
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