Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,40}

Atlas Canonical Name {4,40}*1920c

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1920,240857)
Rank
3
Schläfli Type
{4,40}
Vertices, edges, …
24, 480, 240
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 := ( 1,57)( 2,58)( 3,66)( 4,65)( 5,85)( 6,86)( 7,80)( 8,79)( 9,51)(10,52)(11,73)(12,74)(13,87)(14,88)(15,54)(16,53)(17,50)(18,49)(19,90)(20,89)(21,76)(22,75)(23,60)(24,59)(25,84)(26,83)(27,56)(28,55)(29,77)(30,78)(31,70)(32,69)(33,82)(34,81)(35,71)(36,72)(37,92)(38,91)(39,62)(40,61)(41,67)(42,68)(43,63)(44,64)(45,94)(46,93)(47,95)(48,96);;
s1 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)(23,71)(24,72)(25,73)(26,74)(27,75)(28,76)(29,77)(30,78)(31,79)(32,80)(33,81)(34,82)(35,83)(36,84)(37,85)(38,86)(39,87)(40,88)(41,89)(42,90)(43,91)(44,92)(45,93)(46,94)(47,95)(48,96);;
s2 := ( 1,53)( 2,54)( 3,95)( 4,96)( 5,94)( 6,93)( 7,71)( 8,72)( 9,84)(10,83)(11,62)(12,61)(13,91)(14,92)(15,58)(16,57)(17,67)(18,68)(19,55)(20,56)(21,77)(22,78)(23,81)(24,82)(25,51)(26,52)(27,89)(28,90)(29,76)(30,75)(31,63)(32,64)(33,59)(34,60)(35,80)(36,79)(37,88)(38,87)(39,73)(40,74)(41,50)(42,49)(43,70)(44,69)(45,85)(46,86)(47,66)(48,65);;
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*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(96)!( 1,57)( 2,58)( 3,66)( 4,65)( 5,85)( 6,86)( 7,80)( 8,79)( 9,51)(10,52)(11,73)(12,74)(13,87)(14,88)(15,54)(16,53)(17,50)(18,49)(19,90)(20,89)(21,76)(22,75)(23,60)(24,59)(25,84)(26,83)(27,56)(28,55)(29,77)(30,78)(31,70)(32,69)(33,82)(34,81)(35,71)(36,72)(37,92)(38,91)(39,62)(40,61)(41,67)(42,68)(43,63)(44,64)(45,94)(46,93)(47,95)(48,96);
s1 := Sym(96)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)(23,71)(24,72)(25,73)(26,74)(27,75)(28,76)(29,77)(30,78)(31,79)(32,80)(33,81)(34,82)(35,83)(36,84)(37,85)(38,86)(39,87)(40,88)(41,89)(42,90)(43,91)(44,92)(45,93)(46,94)(47,95)(48,96);
s2 := Sym(96)!( 1,53)( 2,54)( 3,95)( 4,96)( 5,94)( 6,93)( 7,71)( 8,72)( 9,84)(10,83)(11,62)(12,61)(13,91)(14,92)(15,58)(16,57)(17,67)(18,68)(19,55)(20,56)(21,77)(22,78)(23,81)(24,82)(25,51)(26,52)(27,89)(28,90)(29,76)(30,75)(31,63)(32,64)(33,59)(34,60)(35,80)(36,79)(37,88)(38,87)(39,73)(40,74)(41,50)(42,49)(43,70)(44,69)(45,85)(46,86)(47,66)(48,65);
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;

References

None.

to this polytope.

Twisty Puzzle