Polytope of Type {10,2,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,6,8}*1920
if this polytope has a name.
Group : SmallGroup(1920,235343)
Rank : 5
Schlafli Type : {10,2,6,8}
Number of vertices, edges, etc : 10, 10, 6, 24, 8
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 : {5,2,6,8}*960, {10,2,6,4}*960a
   3-fold quotients : {10,2,2,8}*640
   4-fold quotients : {5,2,6,4}*480a, {10,2,6,2}*480
   5-fold quotients : {2,2,6,8}*384
   6-fold quotients : {5,2,2,8}*320, {10,2,2,4}*320
   8-fold quotients : {5,2,6,2}*240, {10,2,3,2}*240
   10-fold quotients : {2,2,6,4}*192a
   12-fold quotients : {5,2,2,4}*160, {10,2,2,2}*160
   15-fold quotients : {2,2,2,8}*128
   16-fold quotients : {5,2,3,2}*120
   20-fold quotients : {2,2,6,2}*96
   24-fold quotients : {5,2,2,2}*80
   30-fold quotients : {2,2,2,4}*64
   40-fold quotients : {2,2,3,2}*48
   60-fold quotients : {2,2,2,2}*32
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 := (13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(33,34);;
s3 := (11,13)(12,19)(15,16)(17,20)(18,25)(21,22)(23,26)(24,31)(27,28)(29,32)
(30,33);;
s4 := (11,12)(13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(25,28)(26,29)(27,30)
(31,33)(32,34);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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(34)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(34)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(34)!(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(33,34);
s3 := Sym(34)!(11,13)(12,19)(15,16)(17,20)(18,25)(21,22)(23,26)(24,31)(27,28)
(29,32)(30,33);
s4 := Sym(34)!(11,12)(13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(25,28)(26,29)
(27,30)(31,33)(32,34);
poly := sub<Sym(34)|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*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope