Part of the Atlas of Small Regular Polytopes

Polytope of Type {9,9}

Atlas Canonical Name {9,9}*1152

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1152,157853)
Rank
3
Schläfli Type
{9,9}
Vertices, edges, …
64, 288, 64
Order of s0s1s2
4
Order of s0s1s2s1
9
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Self-Dual

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^3*s1*s0*s1> of order 2

32 facets

32 vertex figures

P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s1*s0*s2*s1*s0*s1> of order 2

32 facets

32 vertex figures

P/N, where N=<(s0*s1)^4*s0*(s2*s1)^2*(s0*s1)^2*s2> of order 2

32 facets

32 vertex figures

P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s0*(s2*s1)^2*s0*s1*s0*s2*s1*s0*s1> of order 4

16 facets

16 vertex figures

P/N, where N=<(s0*s1)^2*s0*(s2*s1)^2*s0*s1*s0*s2*s1, s0*s1*s0*(s2*s1)^2*s0*s1*s0*s2*s1*s0*s1> of order 4

16 facets

16 vertex figures

P/N, where N=<s0*s2*(s1*s0)^2*s2*s1*s0*s1, (s0*s1)^3*s0*s2*s1*s0*s1*s2*s1*s0> of order 4

16 facets

16 vertex figures

P/N, where N=<(s0*s1)^4*s0*(s2*s1)^2*(s0*s1)^2*s2, (s0*s1)^3*s0*(s2*s1)^3*s0*s1*s0*s2*s1> of order 4

16 facets

16 vertex figures

P/N, where N=<(s0*s1)^3*s0*s2*s1*s0*(s1*s2)^2, s0*s1*s0*(s2*s1)^2*s0*s1*s0*s2*s1*s0*s1> of order 4

16 facets

16 vertex figures

P/N, where N=<(s0*s1)^4*s0*(s2*s1)^3*s0*s1*s2, (s0*s1)^3*s0*s2*s1*s0*s1*s2*(s1*s0)^2*s2*s1> of order 4

16 facets

16 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 3, 4)( 5,17)( 6,18)( 7,20)( 8,19)( 9,49)(10,50)(11,52)(12,51)(13,33)(14,34)(15,36)(16,35)(23,24)(25,53)(26,54)(27,56)(28,55)(29,37)(30,38)(31,40)(32,39)(41,61)(42,62)(43,64)(44,63)(47,48)(59,60);;
s1 := ( 2,33)( 3,49)( 4,17)( 6,37)( 7,53)( 8,21)( 9,13)(10,45)(11,61)(12,29)(14,41)(15,57)(16,25)(18,36)(19,52)(22,40)(23,56)(26,48)(27,64)(28,32)(30,44)(31,60)(35,50)(39,54)(42,46)(43,62)(47,58)(59,63);;
s2 := ( 1, 2)( 5,18)( 6,17)( 7,19)( 8,20)( 9,50)(10,49)(11,51)(12,52)(13,34)(14,33)(15,35)(16,36)(21,22)(25,54)(26,53)(27,55)(28,56)(29,38)(30,37)(31,39)(32,40)(41,62)(42,61)(43,63)(44,64)(45,46)(57,58);;
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, s2*s0*s1*s2*s0*s1*s2*s0*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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(64)!( 3, 4)( 5,17)( 6,18)( 7,20)( 8,19)( 9,49)(10,50)(11,52)(12,51)(13,33)(14,34)(15,36)(16,35)(23,24)(25,53)(26,54)(27,56)(28,55)(29,37)(30,38)(31,40)(32,39)(41,61)(42,62)(43,64)(44,63)(47,48)(59,60);
s1 := Sym(64)!( 2,33)( 3,49)( 4,17)( 6,37)( 7,53)( 8,21)( 9,13)(10,45)(11,61)(12,29)(14,41)(15,57)(16,25)(18,36)(19,52)(22,40)(23,56)(26,48)(27,64)(28,32)(30,44)(31,60)(35,50)(39,54)(42,46)(43,62)(47,58)(59,63);
s2 := Sym(64)!( 1, 2)( 5,18)( 6,17)( 7,19)( 8,20)( 9,50)(10,49)(11,51)(12,52)(13,34)(14,33)(15,35)(16,36)(21,22)(25,54)(26,53)(27,55)(28,56)(29,38)(30,37)(31,39)(32,40)(41,62)(42,61)(43,63)(44,64)(45,46)(57,58);
poly := sub<Sym(64)|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, s2*s0*s1*s2*s0*s1*s2*s0*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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;

References

None.

to this polytope.

Twisty Puzzle