Polytope of Type {10,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12}*600
if this polytope has a name.
Group : SmallGroup(600,170)
Rank : 3
Schlafli Type : {10,12}
Number of vertices, edges, etc : 25, 150, 30
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,12,2} of size 1200
Vertex Figure Of :
   {2,10,12} of size 1200
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {10,4}*200
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,12}*1200c
   3-fold covers : {10,36}*1800
Permutation Representation (GAP) :

s0 := ( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)
(14,18)(15,17)(27,30)(28,29)(31,46)(32,50)(33,49)(34,48)(35,47)(36,41)(37,45)
(38,44)(39,43)(40,42)(52,55)(53,54)(56,71)(57,75)(58,74)(59,73)(60,72)(61,66)
(62,70)(63,69)(64,68)(65,67);;
s1 := ( 1, 6)( 2,17)( 4,14)( 5,25)( 7,12)( 8,23)(10,20)(11,21)(13,18)(19,24)
(26,56)(27,67)(28,53)(29,64)(30,75)(31,51)(32,62)(33,73)(34,59)(35,70)(36,71)
(37,57)(38,68)(39,54)(40,65)(41,66)(42,52)(43,63)(44,74)(45,60)(46,61)(47,72)
(48,58)(49,69)(50,55);;
s2 := ( 1,26)( 2,34)( 3,37)( 4,45)( 5,48)( 6,38)( 7,41)( 8,49)( 9,27)(10,35)
(11,50)(12,28)(13,31)(14,39)(15,42)(16,32)(17,40)(18,43)(19,46)(20,29)(21,44)
(22,47)(23,30)(24,33)(25,36)(52,59)(53,62)(54,70)(55,73)(56,63)(57,66)(58,74)
(61,75)(65,67)(69,71);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(75)!( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)
(13,19)(14,18)(15,17)(27,30)(28,29)(31,46)(32,50)(33,49)(34,48)(35,47)(36,41)
(37,45)(38,44)(39,43)(40,42)(52,55)(53,54)(56,71)(57,75)(58,74)(59,73)(60,72)
(61,66)(62,70)(63,69)(64,68)(65,67);
s1 := Sym(75)!( 1, 6)( 2,17)( 4,14)( 5,25)( 7,12)( 8,23)(10,20)(11,21)(13,18)
(19,24)(26,56)(27,67)(28,53)(29,64)(30,75)(31,51)(32,62)(33,73)(34,59)(35,70)
(36,71)(37,57)(38,68)(39,54)(40,65)(41,66)(42,52)(43,63)(44,74)(45,60)(46,61)
(47,72)(48,58)(49,69)(50,55);
s2 := Sym(75)!( 1,26)( 2,34)( 3,37)( 4,45)( 5,48)( 6,38)( 7,41)( 8,49)( 9,27)
(10,35)(11,50)(12,28)(13,31)(14,39)(15,42)(16,32)(17,40)(18,43)(19,46)(20,29)
(21,44)(22,47)(23,30)(24,33)(25,36)(52,59)(53,62)(54,70)(55,73)(56,63)(57,66)
(58,74)(61,75)(65,67)(69,71);
poly := sub<Sym(75)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2 >;

References : None.
to this polytope