Polytope of Type {10,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,6}*960b
if this polytope has a name.
Group : SmallGroup(960,10891)
Rank : 3
Schlafli Type : {10,6}
Number of vertices, edges, etc : 80, 240, 48
Order of s0s1s2 : 10
Order of s0s1s2s1 : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {10,6,2} of size 1920
Vertex Figure Of :
   {2,10,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {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, {20,6}*1920d
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.
      36 facets:
         24 of {5}*10
         12 of {10}*20
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s2> of order 2.
      24 facets:
         24 of {10}*20
      60 vertex figures:
         20 of {6}*12
         40 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 2.
      24 facets:
         24 of {10}*20
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 3.
      16 facets:
         16 of {10}*20
      32 vertex figures:
         24 of {6}*12
         8 of {2}*4

Permutation Representation (GAP) : 
s0 := ( 2,27)( 3,19)( 4,15)( 7,22)( 8,48)( 9,28)(10,43)(11,25)(12,47)(13,35)(14,37)(16,32)(18,21)(23,42)(24,26)(29,36)(30,45)(31,33)(40,41)(44,46);;
s1 := ( 2,10)( 3,11)( 7,37)( 8,23)( 9,25)(12,26)(13,27)(14,28)(18,35)(19,22)(20,47)(21,33)(24,40)(29,41)(30,42)(31,43)(34,46)(36,38)(39,45)(44,48);;
s2 := ( 1,20)( 2,42)( 3,30)( 4,22)( 5,39)( 6,38)( 7,15)( 8,43)( 9,41)(10,48)(11,24)(12,31)(13,29)(14,44)(16,18)(17,34)(19,45)(21,32)(23,27)(25,26)(28,40)(33,47)(35,36)(37,46);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*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*s2*s1*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(48)!( 2,27)( 3,19)( 4,15)( 7,22)( 8,48)( 9,28)(10,43)(11,25)(12,47)(13,35)(14,37)(16,32)(18,21)(23,42)(24,26)(29,36)(30,45)(31,33)(40,41)(44,46);
s1 := Sym(48)!( 2,10)( 3,11)( 7,37)( 8,23)( 9,25)(12,26)(13,27)(14,28)(18,35)(19,22)(20,47)(21,33)(24,40)(29,41)(30,42)(31,43)(34,46)(36,38)(39,45)(44,48);
s2 := Sym(48)!( 1,20)( 2,42)( 3,30)( 4,22)( 5,39)( 6,38)( 7,15)( 8,43)( 9,41)(10,48)(11,24)(12,31)(13,29)(14,44)(16,18)(17,34)(19,45)(21,32)(23,27)(25,26)(28,40)(33,47)(35,36)(37,46);
poly := sub<Sym(48)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*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*s2*s1*s0*s1*s2*s1*s2 >;
References : None.
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