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}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240872)
Rank : 3
Schlafli Type : {10,12}
Number of vertices, edges, etc : 80, 480, 96
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {10,12}*960c, {10,12}*960d, {10,6}*960b
   4-fold quotients : {10,12}*480c, {10,12}*480d, {5,12}*480, {10,6}*480c
   8-fold quotients : {5,6}*240b, {10,3}*240, {10,6}*240c, {10,6}*240d, {10,6}*240e, {10,6}*240f
   16-fold quotients : {5,3}*120, {5,6}*120b, {5,6}*120c, {10,3}*120a, {10,3}*120b
   32-fold quotients : {5,3}*60
   120-fold quotients : {2,4}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 2.
      72 facets:
         48 of {5}*10
         24 of {10}*20
      40 vertex figures:
         40 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 3.
      32 facets:
         32 of {10}*20
      32 vertex figures:
         24 of {12}*24
         8 of {4}*8

Permutation Representation (GAP) :

s0 := ( 1,31)( 2,32)( 3,29)( 4,30)( 5,39)( 6,40)( 7,37)( 8,38)( 9,36)(10,35)(11,34)(12,33)(13,50)(14,49)(15,46)(16,45)(17,43)(18,44)(19,51)(20,52)(21,41)(22,42)(23,48)(24,47)(25,55)(26,56)(27,54)(28,53);;
s1 := ( 1,29)( 2,30)( 3,31)( 4,32)( 5,35)( 6,36)( 7,34)( 8,33)( 9,49)(10,50)(11,52)(12,51)(13,55)(14,56)(15,46)(16,45)(17,43)(18,44)(19,53)(20,54)(21,38)(22,37)(23,39)(24,40)(25,48)(26,47)(27,42)(28,41);;
s2 := ( 3, 4)( 5,11)( 6,12)( 9,10)(13,18)(14,17)(15,22)(16,21)(19,23)(20,24)(27,28)(29,30)(33,40)(34,39)(35,36)(41,45)(42,46)(43,49)(44,50)(47,52)(48,51)(53,54);;
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, s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*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*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(56)!( 1,31)( 2,32)( 3,29)( 4,30)( 5,39)( 6,40)( 7,37)( 8,38)( 9,36)(10,35)(11,34)(12,33)(13,50)(14,49)(15,46)(16,45)(17,43)(18,44)(19,51)(20,52)(21,41)(22,42)(23,48)(24,47)(25,55)(26,56)(27,54)(28,53);
s1 := Sym(56)!( 1,29)( 2,30)( 3,31)( 4,32)( 5,35)( 6,36)( 7,34)( 8,33)( 9,49)(10,50)(11,52)(12,51)(13,55)(14,56)(15,46)(16,45)(17,43)(18,44)(19,53)(20,54)(21,38)(22,37)(23,39)(24,40)(25,48)(26,47)(27,42)(28,41);
s2 := Sym(56)!( 3, 4)( 5,11)( 6,12)( 9,10)(13,18)(14,17)(15,22)(16,21)(19,23)(20,24)(27,28)(29,30)(33,40)(34,39)(35,36)(41,45)(42,46)(43,49)(44,50)(47,52)(48,51)(53,54);
poly := sub<Sym(56)|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, s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*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*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
to this polytope

Polytope of Type {10,12}

Twisty Puzzle