Polytope of Type {10,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12}*960d
if this polytope has a name.
Group : SmallGroup(960,10889)
Rank : 3
Schlafli Type : {10,12}
Number of vertices, edges, etc : 40, 240, 48
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,12,2} of size 1920
Vertex Figure Of :
   {2,10,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,12}*480, {10,6}*480c
   4-fold quotients : {5,6}*240b, {10,3}*240, {10,6}*240c, {10,6}*240d, {10,6}*240e, {10,6}*240f
   8-fold quotients : {5,3}*120, {5,6}*120b, {5,6}*120c, {10,3}*120a, {10,3}*120b
   16-fold quotients : {5,3}*60
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,12}*1920c, {20,12}*1920l, {20,12}*1920m
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

s0 := ( 2,45)( 3,41)( 4,17)( 5,19)( 7,30)( 8,48)( 9,36)(10,47)(11,23)(12,34)(13,22)(14,40)(15,39)(20,26)(21,29)(24,38)(25,37)(27,46)(28,31)(35,42);;
s1 := ( 2, 3)( 4,17)( 5,19)( 7,28)( 8,35)( 9,29)(10,15)(11,26)(12,39)(13,25)(14,27)(20,38)(21,33)(22,44)(23,31)(24,30)(32,42)(34,41)(40,43)(45,47)(49,50);;
s2 := ( 1,32)( 2,46)( 3,13)( 4,12)( 5,31)( 6,44)( 7,40)( 8,38)( 9,47)(10,36)(11,29)(14,30)(15,35)(16,33)(17,34)(18,43)(19,28)(20,25)(21,23)(22,41)(24,48)(26,37)(27,45)(39,42);;
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*s1*s2*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {10,12}

Twisty Puzzle