Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,10}

Atlas Canonical Name {10,10}*1920

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1920,240995)
Rank
3
Schläfli Type
{10,10}
Vertices, edges, …
96, 480, 96
Order of s0s1s2
6
Order of s0s1s2s1
3
Also known as
if this polytope has a name.

Special Properties

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

Quotients maximal quotients in bold

32-fold

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=<s1*s0*s2*(s1*s0)^4*s1*s2*s1> of order 2

56 facets

56 vertex figures

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

48 facets

48 vertex figures

P/N, where N=<(s1*s2)^5, s0*(s1*s2)^4*s1*s0*s2> of order 4

32 facets

32 vertex figures

P/N, where N=<(s0*s1)^5, s0*(s1*s2)^4*s1*s0*s2, s1*s0*(s1*s2)^4*s1*s0*s2*s1> of order 8

18 facets

18 vertex figures

P/N, where N=<(s1*s2)^5, s0*s2*(s1*s0)^4*s1*s2, s1*s0*s2*(s1*s0)^4*s1*s2*s1> of order 8

18 facets

18 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,18)(14,19)(15,17)(16,20);;
s1 := ( 1, 5)( 2, 7)( 3, 8)( 4, 6)( 9,14)(10,13)(11,15)(12,16)(17,20)(18,19);;
s2 := ( 1, 4)( 2, 3)( 5,13)( 6,14)( 7,15)( 8,16)( 9,18)(10,20)(11,17)(12,19);;
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2, 
s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(20)!( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,18)(14,19)(15,17)(16,20);
s1 := Sym(20)!( 1, 5)( 2, 7)( 3, 8)( 4, 6)( 9,14)(10,13)(11,15)(12,16)(17,20)(18,19);
s2 := Sym(20)!( 1, 4)( 2, 3)( 5,13)( 6,14)( 7,15)( 8,16)( 9,18)(10,20)(11,17)(12,19);
poly := sub<Sym(20)|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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2, 
s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2 >;

References

None.

to this polytope.

Twisty Puzzle