Part of the Atlas of Small Regular Polytopes

Polytope of Type {20,6}

Atlas Canonical Name {20,6}*960b

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(960,10877)
Rank
3
Schläfli Type
{20,6}
Vertices, edges, …
80, 240, 24
Order of s0s1s2
8
Order of s0s1s2s1
8
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

120-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle