Part of the Atlas of Small Regular Polytopes

Polytope of Type {20,10}

Atlas Canonical Name {20,10}*1600

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1600,10261)
Rank
3
Schläfli Type
{20,10}
Vertices, edges, …
80, 400, 40
Order of s0s1s2
5
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

5-fold

10-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*s2)^2*s1*s0*(s1*s2)^3*s1*s0*s1*s2> of order 2

24 facets

40 vertex figures

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

20 facets

40 vertex figures

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

20 facets

40 vertex figures

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

12 facets

20 vertex figures

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

14 facets

20 vertex figures

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

12 facets

20 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle