Polytope of Type {30,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6}*1920c
if this polytope has a name.
Group : SmallGroup(1920,238599)
Rank : 3
Schlafli Type : {30,6}
Number of vertices, edges, etc : 160, 480, 32
Order of s₀s₁s₂ : 40
Order of s₀s₁s₂s₁ : 6
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 : {30,6}*480
   5-fold quotients : {6,6}*384d
   8-fold quotients : {15,6}*240
   10-fold quotients : {6,3}*192
   20-fold quotients : {6,6}*96
   40-fold quotients : {3,6}*48, {6,3}*48
   48-fold quotients : {10,2}*40
   80-fold quotients : {3,3}*24
   96-fold quotients : {5,2}*20
   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=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 2.
      16 facets:
         16 of {30}*60
      80 vertex figures:
         80 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 2.
      20 facets:
         8 of {15}*30
         12 of {30}*60
      80 vertex figures:
         80 of {6}*12
   P/N, where N=<s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2> of order 2.
      16 facets:
         16 of {30}*60
      80 vertex figures:
         80 of {6}*12
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2> of order 4.
      8 facets:
         8 of {30}*60
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      8 facets:
         8 of {30}*60
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 4.
      12 facets:
         8 of {15}*30
         4 of {30}*60
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      8 facets:
         8 of {30}*60
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 4.
      8 facets:
         8 of {30}*60
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1> of order 4.
      8 facets:
         8 of {30}*60
      40 vertex figures:
         40 of {6}*12

Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 6)( 9,13)(10,14)(11,16)(12,15)(17,65)(18,66)(19,68)(20,67)(21,70)(22,69)(23,71)(24,72)(25,77)(26,78)(27,80)(28,79)(29,73)(30,74)(31,76)(32,75)(33,49)(34,50)(35,52)(36,51)(37,54)(38,53)(39,55)(40,56)(41,61)(42,62)(43,64)(44,63)(45,57)(46,58)(47,60)(48,59);;
s1 := ( 1,17)( 2,20)( 3,19)( 4,18)( 5,31)( 6,30)( 7,29)( 8,32)( 9,27)(10,26)(11,25)(12,28)(13,23)(14,22)(15,21)(16,24)(33,65)(34,68)(35,67)(36,66)(37,79)(38,78)(39,77)(40,80)(41,75)(42,74)(43,73)(44,76)(45,71)(46,70)(47,69)(48,72)(50,52)(53,63)(54,62)(55,61)(56,64)(57,59);;
s2 := ( 1, 7)( 2, 8)( 3, 6)( 4, 5)(11,12)(15,16)(17,23)(18,24)(19,22)(20,21)(27,28)(31,32)(33,39)(34,40)(35,38)(36,37)(43,44)(47,48)(49,55)(50,56)(51,54)(52,53)(59,60)(63,64)(65,71)(66,72)(67,70)(68,69)(75,76)(79,80);;
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*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(80)!( 3, 4)( 5, 6)( 9,13)(10,14)(11,16)(12,15)(17,65)(18,66)(19,68)(20,67)(21,70)(22,69)(23,71)(24,72)(25,77)(26,78)(27,80)(28,79)(29,73)(30,74)(31,76)(32,75)(33,49)(34,50)(35,52)(36,51)(37,54)(38,53)(39,55)(40,56)(41,61)(42,62)(43,64)(44,63)(45,57)(46,58)(47,60)(48,59);
s1 := Sym(80)!( 1,17)( 2,20)( 3,19)( 4,18)( 5,31)( 6,30)( 7,29)( 8,32)( 9,27)(10,26)(11,25)(12,28)(13,23)(14,22)(15,21)(16,24)(33,65)(34,68)(35,67)(36,66)(37,79)(38,78)(39,77)(40,80)(41,75)(42,74)(43,73)(44,76)(45,71)(46,70)(47,69)(48,72)(50,52)(53,63)(54,62)(55,61)(56,64)(57,59);
s2 := Sym(80)!( 1, 7)( 2, 8)( 3, 6)( 4, 5)(11,12)(15,16)(17,23)(18,24)(19,22)(20,21)(27,28)(31,32)(33,39)(34,40)(35,38)(36,37)(43,44)(47,48)(49,55)(50,56)(51,54)(52,53)(59,60)(63,64)(65,71)(66,72)(67,70)(68,69)(75,76)(79,80);
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*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1 >;

References : None.
to this polytope

Polytope of Type {30,6}

Twisty Puzzle