Polytope of Type {2,56}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,56}*224
if this polytope has a name.
Group : SmallGroup(224,98)
Rank : 3
Schlafli Type : {2,56}
Number of vertices, edges, etc : 2, 56, 56
Order of s₀s₁s₂ : 56
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,56,2} of size 448
   {2,56,4} of size 896
   {2,56,4} of size 896
   {2,56,6} of size 1344
   {2,56,4} of size 1792
   {2,56,8} of size 1792
   {2,56,8} of size 1792
   {2,56,8} of size 1792
   {2,56,8} of size 1792
   {2,56,4} of size 1792
Vertex Figure Of :
   {2,2,56} of size 448
   {3,2,56} of size 672
   {4,2,56} of size 896
   {5,2,56} of size 1120
   {6,2,56} of size 1344
   {7,2,56} of size 1568
   {8,2,56} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,28}*112
   4-fold quotients : {2,14}*56
   7-fold quotients : {2,8}*32
   8-fold quotients : {2,7}*28
   14-fold quotients : {2,4}*16
   28-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,56}*448a, {2,112}*448
   3-fold covers : {6,56}*672, {2,168}*672
   4-fold covers : {4,56}*896a, {8,56}*896a, {8,56}*896b, {4,112}*896a, {4,112}*896b, {2,224}*896
   5-fold covers : {10,56}*1120, {2,280}*1120
   6-fold covers : {6,112}*1344, {12,56}*1344a, {4,168}*1344a, {2,336}*1344
   7-fold covers : {2,392}*1568, {14,56}*1568a, {14,56}*1568b
   8-fold covers : {8,56}*1792a, {4,56}*1792a, {8,56}*1792d, {4,112}*1792a, {4,112}*1792b, {16,56}*1792a, {16,56}*1792b, {8,112}*1792c, {8,112}*1792d, {16,56}*1792d, {8,112}*1792e, {8,112}*1792f, {16,56}*1792f, {4,224}*1792a, {4,224}*1792b, {2,448}*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);;
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*s1*s0*s1, s0*s2*s0*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*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(58)!(1,2);
s1 := Sym(58)!( 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(58)!( 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);
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*s1*s0*s1, s0*s2*s0*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*s1*s2 >;

to this polytope