Part of the Atlas of Small Regular Polytopes

Polytope of Type {20,3}

Atlas Canonical Name {20,3}*480

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Overview

Group
SmallGroup(480,959)
Rank
3
Schläfli Type
{20,3}
Vertices, edges, …
80, 120, 12
Order of s0s1s2
20
Order of s0s1s2s1
20
Also known as
if this polytope has a name.

Special Properties

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

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle