Polytope of Type {10,2,44}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,44}*1760
if this polytope has a name.
Group : SmallGroup(1760,1181)
Rank : 4
Schlafli Type : {10,2,44}
Number of vertices, edges, etc : 10, 10, 44, 44
Order of s₀s₁s₂s₃ : 220
Order of s₀s₁s₂s₃s₂s₁ : 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 : {5,2,44}*880, {10,2,22}*880
   4-fold quotients : {5,2,22}*440, {10,2,11}*440
   5-fold quotients : {2,2,44}*352
   8-fold quotients : {5,2,11}*220
   10-fold quotients : {2,2,22}*176
   11-fold quotients : {10,2,4}*160
   20-fold quotients : {2,2,11}*88
   22-fold quotients : {5,2,4}*80, {10,2,2}*80
   44-fold quotients : {5,2,2}*40
   55-fold quotients : {2,2,4}*32
   110-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (12,13)(14,15)(17,20)(18,19)(21,22)(23,24)(25,28)(26,27)(29,30)(31,32)
(33,36)(34,35)(37,38)(39,40)(41,44)(42,43)(45,46)(47,48)(49,52)(50,51)
(53,54);;
s3 := (11,17)(12,14)(13,23)(15,25)(16,19)(18,21)(20,31)(22,33)(24,27)(26,29)
(28,39)(30,41)(32,35)(34,37)(36,47)(38,49)(40,43)(42,45)(44,53)(46,50)(48,51)
(52,54);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(54)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(54)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(54)!(12,13)(14,15)(17,20)(18,19)(21,22)(23,24)(25,28)(26,27)(29,30)
(31,32)(33,36)(34,35)(37,38)(39,40)(41,44)(42,43)(45,46)(47,48)(49,52)(50,51)
(53,54);
s3 := Sym(54)!(11,17)(12,14)(13,23)(15,25)(16,19)(18,21)(20,31)(22,33)(24,27)
(26,29)(28,39)(30,41)(32,35)(34,37)(36,47)(38,49)(40,43)(42,45)(44,53)(46,50)
(48,51)(52,54);
poly := sub<Sym(54)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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 >;

to this polytope