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Polytope of Type {2,56,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,56,2}*448
if this polytope has a name.
Group : SmallGroup(448,1193)
Rank : 4
Schlafli Type : {2,56,2}
Number of vertices, edges, etc : 2, 56, 56, 2
Order of s0s1s2s3 : 56
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,56,2,2} of size 896
   {2,56,2,3} of size 1344
   {2,56,2,4} of size 1792
Vertex Figure Of :
   {2,2,56,2} of size 896
   {3,2,56,2} of size 1344
   {4,2,56,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,28,2}*224
   4-fold quotients : {2,14,2}*112
   7-fold quotients : {2,8,2}*64
   8-fold quotients : {2,7,2}*56
   14-fold quotients : {2,4,2}*32
   28-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,56,4}*896a, {4,56,2}*896a, {2,112,2}*896
   3-fold covers : {2,56,6}*1344, {6,56,2}*1344, {2,168,2}*1344
   4-fold covers : {2,56,4}*1792a, {4,56,2}*1792a, {2,56,8}*1792b, {2,56,8}*1792c, {8,56,2}*1792b, {8,56,2}*1792c, {4,56,4}*1792d, {2,112,4}*1792a, {4,112,2}*1792a, {2,112,4}*1792b, {4,112,2}*1792b, {2,224,2}*1792
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,23)(18,22)(19,25)
(20,24)(26,27)(29,36)(30,35)(31,38)(32,37)(33,40)(34,39)(41,42)(43,48)(44,47)
(45,50)(46,49)(51,52)(53,56)(54,55)(57,58);;
s2 := ( 3, 9)( 4, 6)( 5,17)( 7,19)( 8,12)(10,14)(11,29)(13,31)(15,33)(16,22)
(18,24)(20,26)(21,41)(23,43)(25,45)(27,34)(28,35)(30,37)(32,39)(36,51)(38,53)
(40,46)(42,47)(44,49)(48,57)(50,54)(52,55)(56,58);;
s3 := (59,60);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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*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*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*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(60)!(1,2);
s1 := Sym(60)!( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,23)(18,22)
(19,25)(20,24)(26,27)(29,36)(30,35)(31,38)(32,37)(33,40)(34,39)(41,42)(43,48)
(44,47)(45,50)(46,49)(51,52)(53,56)(54,55)(57,58);
s2 := Sym(60)!( 3, 9)( 4, 6)( 5,17)( 7,19)( 8,12)(10,14)(11,29)(13,31)(15,33)
(16,22)(18,24)(20,26)(21,41)(23,43)(25,45)(27,34)(28,35)(30,37)(32,39)(36,51)
(38,53)(40,46)(42,47)(44,49)(48,57)(50,54)(52,55)(56,58);
s3 := Sym(60)!(59,60);
poly := sub<Sym(60)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, 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*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*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*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 >; 
 

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