Polytope of Type {4,30}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30}*960a
if this polytope has a name.
Group : SmallGroup(960,6310)
Rank : 3
Schlafli Type : {4,30}
Number of vertices, edges, etc : 16, 240, 120
Order of s0s1s2 : 30
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,30,2} of size 1920
Vertex Figure Of :
   {2,4,30} of size 1920
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {4,30}*240b
   5-fold quotients : {4,6}*192a
   8-fold quotients : {4,15}*120
   20-fold quotients : {4,6}*48c
   40-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,60}*1920b, {4,60}*1920c, {8,30}*1920b, {8,30}*1920c, {4,30}*1920a
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      60 facets:
         60 of {4}*8
      10 vertex figures:
         4 of {15}*30
         6 of {30}*60
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 2.
      60 facets:
         60 of {4}*8
      8 vertex figures:
         8 of {30}*60
   P/N, where N=<s0*s2*s1*s0*s1*s2> of order 2.
      70 facets:
         50 of {4}*8
         20 of {2}*4
      8 vertex figures:
         8 of {30}*60
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 4.
      40 facets:
         20 of {2}*4
         20 of {4}*8
      4 vertex figures:
         4 of {30}*60
   P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      45 facets:
         15 of {4}*8
         30 of {2}*4
      4 vertex figures:
         4 of {30}*60
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      30 facets:
         30 of {4}*8
      6 vertex figures:
         4 of {15}*30
         2 of {30}*60

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