Polytope of Type {10,2,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,12,4}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240141)
Rank : 5
Schlafli Type : {10,2,12,4}
Number of vertices, edges, etc : 10, 10, 12, 24, 4
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {5,2,12,4}*960c, {10,2,6,4}*960c
   4-fold quotients : {5,2,6,4}*480c, {10,2,3,4}*480
   5-fold quotients : {2,2,12,4}*384c
   8-fold quotients : {5,2,3,4}*240
   10-fold quotients : {2,2,6,4}*192c
   20-fold quotients : {2,2,3,4}*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)(16,26)(18,22)(19,21)(20,34)(23,39)(24,42)(25,27)(28,44)
(29,30)(31,47)(32,50)(33,40)(35,38)(36,54)(37,51)(41,53)(45,56)(46,48)(49,58)
(52,55);;
s3 := (11,18)(12,14)(13,29)(15,19)(16,53)(17,21)(20,44)(22,30)(23,58)(24,52)
(25,36)(26,35)(27,39)(28,33)(31,54)(32,43)(34,48)(37,57)(38,49)(40,47)(41,46)
(42,51)(45,55)(50,56);;
s4 := (11,57)(12,55)(13,52)(14,58)(15,49)(16,47)(17,43)(18,54)(19,41)(20,34)
(21,53)(22,36)(23,39)(24,48)(25,56)(26,31)(27,45)(28,30)(29,44)(32,40)(33,50)
(35,37)(38,51)(42,46);;
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, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s2, 
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)(16,26)(18,22)(19,21)(20,34)(23,39)(24,42)(25,27)
(28,44)(29,30)(31,47)(32,50)(33,40)(35,38)(36,54)(37,51)(41,53)(45,56)(46,48)
(49,58)(52,55);
s3 := Sym(58)!(11,18)(12,14)(13,29)(15,19)(16,53)(17,21)(20,44)(22,30)(23,58)
(24,52)(25,36)(26,35)(27,39)(28,33)(31,54)(32,43)(34,48)(37,57)(38,49)(40,47)
(41,46)(42,51)(45,55)(50,56);
s4 := Sym(58)!(11,57)(12,55)(13,52)(14,58)(15,49)(16,47)(17,43)(18,54)(19,41)
(20,34)(21,53)(22,36)(23,39)(24,48)(25,56)(26,31)(27,45)(28,30)(29,44)(32,40)
(33,50)(35,37)(38,51)(42,46);
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, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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