Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,20}

Atlas Canonical Name {10,20}*1600

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1600,10261)
Rank
3
Schläfli Type
{10,20}
Vertices, edges, …
40, 400, 80
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=<(s0*s1)^3*s2*(s1*s0)^3*s1*s2*s1> of order 2

40 facets

24 vertex figures

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

40 facets

20 vertex figures

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

40 facets

20 vertex figures

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

20 facets

14 vertex figures

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

20 facets

12 vertex figures

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

20 facets

12 vertex figures

Representations

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

References

None.

to this polytope.

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