Part of the Atlas of Small Regular Polytopes

Polytope of Type {15,8}

Atlas Canonical Name {15,8}*960a

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(960,6311)
Rank
3
Schläfli Type
{15,8}
Vertices, edges, …
60, 240, 32
Order of s0s1s2
30
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

4-fold

5-fold

8-fold

16-fold

20-fold

40-fold

48-fold

80-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

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

16 facets

40 vertex figures

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

16 facets

30 vertex figures

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

8 facets

30 vertex figures

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

8 facets

20 vertex figures

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

8 facets

20 vertex figures

Representations

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

Twisty Puzzle