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Polytope of Type {4,2,56,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,56,2}*1792
if this polytope has a name.
Group : SmallGroup(1792,1044763)
Rank : 5
Schlafli Type : {4,2,56,2}
Number of vertices, edges, etc : 4, 4, 56, 56, 2
Order of s0s1s2s3s4 : 56
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
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 : {4,2,28,2}*896, {2,2,56,2}*896
4-fold quotients : {2,2,28,2}*448, {4,2,14,2}*448
7-fold quotients : {4,2,8,2}*256
8-fold quotients : {4,2,7,2}*224, {2,2,14,2}*224
14-fold quotients : {4,2,4,2}*128, {2,2,8,2}*128
16-fold quotients : {2,2,7,2}*112
28-fold quotients : {2,2,4,2}*64, {4,2,2,2}*64
56-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,17)(18,23)(19,25)(20,24)(21,27)
(22,26)(28,29)(31,38)(32,37)(33,40)(34,39)(35,42)(36,41)(43,44)(45,50)(46,49)
(47,52)(48,51)(53,54)(55,58)(56,57)(59,60);;
s3 := ( 5,11)( 6, 8)( 7,19)( 9,21)(10,14)(12,16)(13,31)(15,33)(17,35)(18,24)
(20,26)(22,28)(23,43)(25,45)(27,47)(29,36)(30,37)(32,39)(34,41)(38,53)(40,55)
(42,48)(44,49)(46,51)(50,59)(52,56)(54,57)(58,60);;
s4 := (61,62);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(62)!(2,3);
s1 := Sym(62)!(1,2)(3,4);
s2 := Sym(62)!( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,17)(18,23)(19,25)(20,24)
(21,27)(22,26)(28,29)(31,38)(32,37)(33,40)(34,39)(35,42)(36,41)(43,44)(45,50)
(46,49)(47,52)(48,51)(53,54)(55,58)(56,57)(59,60);
s3 := Sym(62)!( 5,11)( 6, 8)( 7,19)( 9,21)(10,14)(12,16)(13,31)(15,33)(17,35)
(18,24)(20,26)(22,28)(23,43)(25,45)(27,47)(29,36)(30,37)(32,39)(34,41)(38,53)
(40,55)(42,48)(44,49)(46,51)(50,59)(52,56)(54,57)(58,60);
s4 := Sym(62)!(61,62);
poly := sub<Sym(62)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope