Polytope of Type {40,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,6}*1920c
if this polytope has a name.
Group : SmallGroup(1920,238599)
Rank : 3
Schlafli Type : {40,6}
Number of vertices, edges, etc : 160, 480, 24
Order of s0s1s2 : 30
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {20,6}*480c
   5-fold quotients : {8,6}*384e
   8-fold quotients : {20,6}*240b
   10-fold quotients : {8,3}*192
   16-fold quotients : {10,6}*120
   20-fold quotients : {4,6}*96
   40-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {10,2}*40
   80-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {5,2}*20
   160-fold quotients : {2,3}*12
   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*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0> of order 2.
      12 facets:
         12 of {40}*80
      80 vertex figures:
         80 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2> of order 2.
      16 facets:
         8 of {20}*40
         8 of {40}*80
      80 vertex figures:
         80 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1> of order 2.
      12 facets:
         12 of {40}*80
      80 vertex figures:
         80 of {6}*12
   P/N, where N=<s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 4.
      8 facets:
         4 of {20}*40
         4 of {40}*80
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1, s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 4.
      8 facets:
         4 of {20}*40
         4 of {40}*80
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      12 facets:
         8 of {10}*20
         4 of {40}*80
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s0*s1, s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0> of order 4.
      8 facets:
         4 of {20}*40
         4 of {40}*80
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2> of order 4.
      8 facets:
         4 of {20}*40
         4 of {40}*80
      40 vertex figures:
         40 of {6}*12

Permutation Representation (GAP) : 
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,14)( 6,13)( 7,16)( 8,15)(17,73)(18,74)(19,75)(20,76)(21,78)(22,77)(23,80)(24,79)(25,65)(26,66)(27,67)(28,68)(29,70)(30,69)(31,72)(32,71)(33,57)(34,58)(35,59)(36,60)(37,62)(38,61)(39,64)(40,63)(41,49)(42,50)(43,51)(44,52)(45,54)(46,53)(47,56)(48,55);;
s1 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,22)( 6,21)( 7,23)( 8,24)( 9,29)(10,30)(11,32)(12,31)(13,25)(14,26)(15,28)(16,27)(33,65)(34,66)(35,68)(36,67)(37,70)(38,69)(39,71)(40,72)(41,77)(42,78)(43,80)(44,79)(45,73)(46,74)(47,76)(48,75)(51,52)(53,54)(57,61)(58,62)(59,64)(60,63);;
s2 := ( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(18,20)(21,30)(22,31)(23,32)(24,29)(26,28)(34,36)(37,46)(38,47)(39,48)(40,45)(42,44)(50,52)(53,62)(54,63)(55,64)(56,61)(58,60)(66,68)(69,78)(70,79)(71,80)(72,77)(74,76);;
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*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(80)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,14)( 6,13)( 7,16)( 8,15)(17,73)(18,74)(19,75)(20,76)(21,78)(22,77)(23,80)(24,79)(25,65)(26,66)(27,67)(28,68)(29,70)(30,69)(31,72)(32,71)(33,57)(34,58)(35,59)(36,60)(37,62)(38,61)(39,64)(40,63)(41,49)(42,50)(43,51)(44,52)(45,54)(46,53)(47,56)(48,55);
s1 := Sym(80)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,22)( 6,21)( 7,23)( 8,24)( 9,29)(10,30)(11,32)(12,31)(13,25)(14,26)(15,28)(16,27)(33,65)(34,66)(35,68)(36,67)(37,70)(38,69)(39,71)(40,72)(41,77)(42,78)(43,80)(44,79)(45,73)(46,74)(47,76)(48,75)(51,52)(53,54)(57,61)(58,62)(59,64)(60,63);
s2 := Sym(80)!( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(18,20)(21,30)(22,31)(23,32)(24,29)(26,28)(34,36)(37,46)(38,47)(39,48)(40,45)(42,44)(50,52)(53,62)(54,63)(55,64)(56,61)(58,60)(66,68)(69,78)(70,79)(71,80)(72,77)(74,76);
poly := sub<Sym(80)|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*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 >;
References : None.
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