Part of the Atlas of Small Regular Polytopes

Polytope of Type {40,4}

Atlas Canonical Name {40,4}*1920c

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1920,240857)
Rank
3
Schläfli Type
{40,4}
Vertices, edges, …
240, 480, 24
Order of s0s1s2
12
Order of s0s1s2s1
12
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

16-fold

240-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := ( 1,53)( 2,54)( 3,92)( 4,91)( 5,55)( 6,56)( 7,71)( 8,72)( 9,86)(10,85)(11,58)(12,57)(13,67)(14,68)(15,76)(16,75)(17,64)(18,63)(19,87)(20,88)(21,74)(22,73)(23,50)(24,49)(25,51)(26,52)(27,83)(28,84)(29,81)(30,82)(31,60)(32,59)(33,96)(34,95)(35,66)(36,65)(37,79)(38,80)(39,89)(40,90)(41,62)(42,61)(43,70)(44,69)(45,78)(46,77)(47,94)(48,93);;
s1 := ( 1,51)( 2,52)( 3,57)( 4,58)( 5,63)( 6,64)( 7,69)( 8,70)( 9,55)(10,56)(11,77)(12,78)(13,76)(14,75)(15,74)(16,73)(17,81)(18,82)(19,60)(20,59)(21,80)(22,79)(23,84)(24,83)(25,72)(26,71)(27,93)(28,94)(29,90)(30,89)(31,49)(32,50)(33,62)(34,61)(35,92)(36,91)(37,96)(38,95)(39,65)(40,66)(41,86)(42,85)(43,54)(44,53)(45,88)(46,87)(47,68)(48,67);;
s2 := ( 1,55)( 2,56)( 3,52)( 4,51)( 5,53)( 6,54)( 7,50)( 8,49)( 9,87)(10,88)(11,77)(12,78)(13,66)(14,65)(15,89)(16,90)(17,82)(18,81)(19,86)(20,85)(21,70)(22,69)(23,71)(24,72)(25,91)(26,92)(27,94)(28,93)(29,63)(30,64)(31,61)(32,62)(33,79)(34,80)(35,67)(36,68)(37,96)(38,95)(39,76)(40,75)(41,59)(42,60)(43,74)(44,73)(45,57)(46,58)(47,83)(48,84);;
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, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(96)!( 1,53)( 2,54)( 3,92)( 4,91)( 5,55)( 6,56)( 7,71)( 8,72)( 9,86)(10,85)(11,58)(12,57)(13,67)(14,68)(15,76)(16,75)(17,64)(18,63)(19,87)(20,88)(21,74)(22,73)(23,50)(24,49)(25,51)(26,52)(27,83)(28,84)(29,81)(30,82)(31,60)(32,59)(33,96)(34,95)(35,66)(36,65)(37,79)(38,80)(39,89)(40,90)(41,62)(42,61)(43,70)(44,69)(45,78)(46,77)(47,94)(48,93);
s1 := Sym(96)!( 1,51)( 2,52)( 3,57)( 4,58)( 5,63)( 6,64)( 7,69)( 8,70)( 9,55)(10,56)(11,77)(12,78)(13,76)(14,75)(15,74)(16,73)(17,81)(18,82)(19,60)(20,59)(21,80)(22,79)(23,84)(24,83)(25,72)(26,71)(27,93)(28,94)(29,90)(30,89)(31,49)(32,50)(33,62)(34,61)(35,92)(36,91)(37,96)(38,95)(39,65)(40,66)(41,86)(42,85)(43,54)(44,53)(45,88)(46,87)(47,68)(48,67);
s2 := Sym(96)!( 1,55)( 2,56)( 3,52)( 4,51)( 5,53)( 6,54)( 7,50)( 8,49)( 9,87)(10,88)(11,77)(12,78)(13,66)(14,65)(15,89)(16,90)(17,82)(18,81)(19,86)(20,85)(21,70)(22,69)(23,71)(24,72)(25,91)(26,92)(27,94)(28,93)(29,63)(30,64)(31,61)(32,62)(33,79)(34,80)(35,67)(36,68)(37,96)(38,95)(39,76)(40,75)(41,59)(42,60)(43,74)(44,73)(45,57)(46,58)(47,83)(48,84);
poly := sub<Sym(96)|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, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.

Twisty Puzzle