Polytope of Type {10,2,3,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,3,12}*1920
if this polytope has a name.
Group : SmallGroup(1920,240195)
Rank : 5
Schlafli Type : {10,2,3,12}
Number of vertices, edges, etc : 10, 10, 4, 24, 16
Order of s₀s₁s₂s₃s₄ : 40
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 : {5,2,3,12}*960, {10,2,3,6}*960
   4-fold quotients : {5,2,3,6}*480, {10,2,3,3}*480
   5-fold quotients : {2,2,3,12}*384
   8-fold quotients : {5,2,3,3}*240
   10-fold quotients : {2,2,3,6}*192
   20-fold quotients : {2,2,3,3}*96
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)(16,29)(17,32)(19,24)(20,23)(21,41)(22,44)(25,47)(26,48)
(27,33)(28,30)(31,52)(34,51)(35,36)(37,53)(38,55)(39,42)(40,45)(43,57)(46,58)
(49,50);;
s3 := (11,14)(12,23)(13,19)(16,52)(17,51)(18,35)(20,24)(21,57)(22,58)(25,50)
(26,49)(27,34)(28,31)(29,30)(32,33)(37,54)(38,56)(39,43)(40,46)(41,42)(44,45)
(47,48);;
s4 := (11,54)(12,49)(13,50)(14,43)(15,57)(16,22)(17,21)(18,56)(19,31)(20,51)
(23,34)(24,52)(25,40)(26,39)(27,38)(28,37)(29,44)(30,53)(32,41)(33,55)(35,46)
(36,58)(42,48)(45,47);;
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*s2*s3*s2*s3, s4*s2*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3, 
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(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)(16,29)(17,32)(19,24)(20,23)(21,41)(22,44)(25,47)
(26,48)(27,33)(28,30)(31,52)(34,51)(35,36)(37,53)(38,55)(39,42)(40,45)(43,57)
(46,58)(49,50);
s3 := Sym(58)!(11,14)(12,23)(13,19)(16,52)(17,51)(18,35)(20,24)(21,57)(22,58)
(25,50)(26,49)(27,34)(28,31)(29,30)(32,33)(37,54)(38,56)(39,43)(40,46)(41,42)
(44,45)(47,48);
s4 := Sym(58)!(11,54)(12,49)(13,50)(14,43)(15,57)(16,22)(17,21)(18,56)(19,31)
(20,51)(23,34)(24,52)(25,40)(26,39)(27,38)(28,37)(29,44)(30,53)(32,41)(33,55)
(35,46)(36,58)(42,48)(45,47);
poly := sub<Sym(58)|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*s2*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope