Polytope of Type {10,2,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,48}*1920
if this polytope has a name.
Group : SmallGroup(1920,203905)
Rank : 4
Schlafli Type : {10,2,48}
Number of vertices, edges, etc : 10, 10, 48, 48
Order of s₀s₁s₂s₃ : 240
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 : {5,2,48}*960, {10,2,24}*960
   3-fold quotients : {10,2,16}*640
   4-fold quotients : {5,2,24}*480, {10,2,12}*480
   5-fold quotients : {2,2,48}*384
   6-fold quotients : {5,2,16}*320, {10,2,8}*320
   8-fold quotients : {5,2,12}*240, {10,2,6}*240
   10-fold quotients : {2,2,24}*192
   12-fold quotients : {5,2,8}*160, {10,2,4}*160
   15-fold quotients : {2,2,16}*128
   16-fold quotients : {5,2,6}*120, {10,2,3}*120
   20-fold quotients : {2,2,12}*96
   24-fold quotients : {5,2,4}*80, {10,2,2}*80
   30-fold quotients : {2,2,8}*64
   32-fold quotients : {5,2,3}*60
   40-fold quotients : {2,2,6}*48
   48-fold quotients : {5,2,2}*40
   60-fold quotients : {2,2,4}*32
   80-fold quotients : {2,2,3}*24
   120-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)(16,19)(17,21)(18,20)(22,25)(23,27)(24,26)(28,31)(29,33)
(30,32)(34,37)(35,39)(36,38)(40,43)(41,45)(42,44)(46,49)(47,51)(48,50)(53,56)
(54,55)(57,58);;
s3 := (11,17)(12,14)(13,23)(15,18)(16,20)(19,29)(21,24)(22,26)(25,35)(27,30)
(28,32)(31,41)(33,36)(34,38)(37,47)(39,42)(40,44)(43,53)(45,48)(46,50)(49,57)
(51,54)(52,55)(56,58);;
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*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(58)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(58)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(58)!(12,13)(14,15)(16,19)(17,21)(18,20)(22,25)(23,27)(24,26)(28,31)
(29,33)(30,32)(34,37)(35,39)(36,38)(40,43)(41,45)(42,44)(46,49)(47,51)(48,50)
(53,56)(54,55)(57,58);
s3 := Sym(58)!(11,17)(12,14)(13,23)(15,18)(16,20)(19,29)(21,24)(22,26)(25,35)
(27,30)(28,32)(31,41)(33,36)(34,38)(37,47)(39,42)(40,44)(43,53)(45,48)(46,50)
(49,57)(51,54)(52,55)(56,58);
poly := sub<Sym(58)|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*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope