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Polytope of Type {56,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56,2}*224
if this polytope has a name.
Group : SmallGroup(224,98)
Rank : 3
Schlafli Type : {56,2}
Number of vertices, edges, etc : 56, 56, 2
Order of s0s1s2 : 56
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {56,2,2} of size 448
   {56,2,3} of size 672
   {56,2,4} of size 896
   {56,2,5} of size 1120
   {56,2,6} of size 1344
   {56,2,7} of size 1568
   {56,2,8} of size 1792
Vertex Figure Of :
   {2,56,2} of size 448
   {4,56,2} of size 896
   {4,56,2} of size 896
   {6,56,2} of size 1344
   {4,56,2} of size 1792
   {8,56,2} of size 1792
   {8,56,2} of size 1792
   {8,56,2} of size 1792
   {8,56,2} of size 1792
   {4,56,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {28,2}*112
   4-fold quotients : {14,2}*56
   7-fold quotients : {8,2}*32
   8-fold quotients : {7,2}*28
   14-fold quotients : {4,2}*16
   28-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {56,4}*448a, {112,2}*448
   3-fold covers : {56,6}*672, {168,2}*672
   4-fold covers : {56,4}*896a, {56,8}*896a, {56,8}*896b, {112,4}*896a, {112,4}*896b, {224,2}*896
   5-fold covers : {56,10}*1120, {280,2}*1120
   6-fold covers : {112,6}*1344, {56,12}*1344a, {168,4}*1344a, {336,2}*1344
   7-fold covers : {392,2}*1568, {56,14}*1568a, {56,14}*1568b
   8-fold covers : {56,8}*1792a, {56,4}*1792a, {56,8}*1792d, {112,4}*1792a, {112,4}*1792b, {56,16}*1792a, {56,16}*1792b, {112,8}*1792c, {112,8}*1792d, {56,16}*1792d, {112,8}*1792e, {112,8}*1792f, {56,16}*1792f, {224,4}*1792a, {224,4}*1792b, {448,2}*1792
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)(17,23)
(18,22)(24,25)(27,34)(28,33)(29,36)(30,35)(31,38)(32,37)(39,40)(41,46)(42,45)
(43,48)(44,47)(49,50)(51,54)(52,53)(55,56);;
s1 := ( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,27)(11,29)(13,31)(14,20)
(16,22)(18,24)(19,39)(21,41)(23,43)(25,32)(26,33)(28,35)(30,37)(34,49)(36,51)
(38,44)(40,45)(42,47)(46,55)(48,52)(50,53)(54,56);;
s2 := (57,58);;
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, 
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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(58)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)
(17,23)(18,22)(24,25)(27,34)(28,33)(29,36)(30,35)(31,38)(32,37)(39,40)(41,46)
(42,45)(43,48)(44,47)(49,50)(51,54)(52,53)(55,56);
s1 := Sym(58)!( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,27)(11,29)(13,31)
(14,20)(16,22)(18,24)(19,39)(21,41)(23,43)(25,32)(26,33)(28,35)(30,37)(34,49)
(36,51)(38,44)(40,45)(42,47)(46,55)(48,52)(50,53)(54,56);
s2 := Sym(58)!(57,58);
poly := sub<Sym(58)|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, 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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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