Polytope of Type {2,24,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,2,10}*1920
if this polytope has a name.
Group : SmallGroup(1920,235347)
Rank : 5
Schlafli Type : {2,24,2,10}
Number of vertices, edges, etc : 2, 24, 24, 10, 10
Order of s₀s₁s₂s₃s₄ : 120
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 : {2,24,2,5}*960, {2,12,2,10}*960
   3-fold quotients : {2,8,2,10}*640
   4-fold quotients : {2,12,2,5}*480, {2,6,2,10}*480
   5-fold quotients : {2,24,2,2}*384
   6-fold quotients : {2,8,2,5}*320, {2,4,2,10}*320
   8-fold quotients : {2,3,2,10}*240, {2,6,2,5}*240
   10-fold quotients : {2,12,2,2}*192
   12-fold quotients : {2,4,2,5}*160, {2,2,2,10}*160
   15-fold quotients : {2,8,2,2}*128
   16-fold quotients : {2,3,2,5}*120
   20-fold quotients : {2,6,2,2}*96
   24-fold quotients : {2,2,2,5}*80
   30-fold quotients : {2,4,2,2}*64
   40-fold quotients : {2,3,2,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,17)(15,19)(16,18)(21,24)(22,23)
(25,26);;
s2 := ( 3, 9)( 4, 6)( 5,15)( 7,10)( 8,12)(11,21)(13,16)(14,18)(17,25)(19,22)
(20,23)(24,26);;
s3 := (29,30)(31,32)(33,34)(35,36);;
s4 := (27,31)(28,29)(30,35)(32,33)(34,36);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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(36)!(1,2);
s1 := Sym(36)!( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,17)(15,19)(16,18)(21,24)
(22,23)(25,26);
s2 := Sym(36)!( 3, 9)( 4, 6)( 5,15)( 7,10)( 8,12)(11,21)(13,16)(14,18)(17,25)
(19,22)(20,23)(24,26);
s3 := Sym(36)!(29,30)(31,32)(33,34)(35,36);
s4 := Sym(36)!(27,31)(28,29)(30,35)(32,33)(34,36);
poly := sub<Sym(36)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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