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

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

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