Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,20}

Atlas Canonical Name {4,20}*160

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(160,103)
Rank
3
Schläfli Type
{4,20}
Vertices, edges, …
4, 40, 20
Order of s0s1s2
20
Order of s0s1s2s1
2
Also known as
{4,20|2}. if this polytope has another name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

5-fold

8-fold

10-fold

20-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

9-fold

10-fold

11-fold

12-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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