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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,10,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,235343)
Rank : 5
Schlafli Type : {8,2,10,6}
Number of vertices, edges, etc : 8, 8, 10, 30, 6
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 : {4,2,10,6}*960
   3-fold quotients : {8,2,10,2}*640
   4-fold quotients : {2,2,10,6}*480
   5-fold quotients : {8,2,2,6}*384
   6-fold quotients : {8,2,5,2}*320, {4,2,10,2}*320
   10-fold quotients : {8,2,2,3}*192, {4,2,2,6}*192
   12-fold quotients : {4,2,5,2}*160, {2,2,10,2}*160
   15-fold quotients : {8,2,2,2}*128
   20-fold quotients : {4,2,2,3}*96, {2,2,2,6}*96
   24-fold quotients : {2,2,5,2}*80
   30-fold quotients : {4,2,2,2}*64
   40-fold quotients : {2,2,2,3}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (13,14)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)
(35,36)(37,38);;
s3 := ( 9,13)(10,17)(11,21)(12,19)(14,23)(15,27)(16,25)(18,29)(20,33)(22,31)
(26,37)(28,35)(32,34)(36,38);;
s4 := ( 9,15)(10,11)(12,16)(13,25)(14,26)(17,19)(18,20)(21,27)(22,28)(23,35)
(24,36)(29,31)(30,32)(33,37)(34,38);;
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, 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, 
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(38)!(2,3)(4,5)(6,7);
s1 := Sym(38)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(38)!(13,14)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)
(33,34)(35,36)(37,38);
s3 := Sym(38)!( 9,13)(10,17)(11,21)(12,19)(14,23)(15,27)(16,25)(18,29)(20,33)
(22,31)(26,37)(28,35)(32,34)(36,38);
s4 := Sym(38)!( 9,15)(10,11)(12,16)(13,25)(14,26)(17,19)(18,20)(21,27)(22,28)
(23,35)(24,36)(29,31)(30,32)(33,37)(34,38);
poly := sub<Sym(38)|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, 
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope