Part of the Atlas of Small Regular Polytopes

Polytope of Type {20,4}

Atlas Canonical Name {20,4}*800

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(800,1058)
Rank
3
Schläfli Type
{20,4}
Vertices, edges, …
100, 200, 20
Order of s0s1s2
4
Order of s0s1s2s1
10
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

25-fold

50-fold

100-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=<(s0*s1)^5*s2*(s1*s0)^4*s1*s2> of order 2

10 facets

50 vertex figures

P/N, where N=<(s0*s1)^4> of order 5

12 facets

20 vertex figures

P/N, where N=<(s0*s1)^5*s2*s1*s0*s1*s2*s1> of order 5

4 facets

20 vertex figures

P/N, where N=<(s1*s0*s1*s2)^2> of order 5

4 facets

20 vertex figures

Representations

Permutation Representation (GAP) 
s0 := (  1, 51)(  2, 55)(  3, 54)(  4, 53)(  5, 52)(  6, 71)(  7, 75)(  8, 74)(  9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)( 16, 61)( 17, 65)( 18, 64)( 19, 63)( 20, 62)( 21, 56)( 22, 60)( 23, 59)( 24, 58)( 25, 57)( 26, 76)( 27, 80)( 28, 79)( 29, 78)( 30, 77)( 31, 96)( 32,100)( 33, 99)( 34, 98)( 35, 97)( 36, 91)( 37, 95)( 38, 94)( 39, 93)( 40, 92)( 41, 86)( 42, 90)( 43, 89)( 44, 88)( 45, 87)( 46, 81)( 47, 85)( 48, 84)( 49, 83)( 50, 82);;
s1 := (  1, 12)(  2, 24)(  3,  6)(  4, 18)(  7, 15)(  8, 22)( 10, 16)( 11, 19)( 14, 25)( 20, 23)( 26, 37)( 27, 49)( 28, 31)( 29, 43)( 32, 40)( 33, 47)( 35, 41)( 36, 44)( 39, 50)( 45, 48)( 51, 87)( 52, 99)( 53, 81)( 54, 93)( 55, 80)( 56, 78)( 57, 90)( 58, 97)( 59, 84)( 60, 91)( 61, 94)( 62, 76)( 63, 88)( 64,100)( 65, 82)( 66, 85)( 67, 92)( 68, 79)( 69, 86)( 70, 98)( 71, 96)( 72, 83)( 73, 95)( 74, 77)( 75, 89);;
s2 := (  2,  7)(  3, 13)(  4, 19)(  5, 25)(  6, 21)(  9, 14)( 10, 20)( 11, 16)( 12, 22)( 18, 23)( 27, 32)( 28, 38)( 29, 44)( 30, 50)( 31, 46)( 34, 39)( 35, 45)( 36, 41)( 37, 47)( 43, 48)( 52, 57)( 53, 63)( 54, 69)( 55, 75)( 56, 71)( 59, 64)( 60, 70)( 61, 66)( 62, 72)( 68, 73)( 77, 82)( 78, 88)( 79, 94)( 80,100)( 81, 96)( 84, 89)( 85, 95)( 86, 91)( 87, 97)( 93, 98);;
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, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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*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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(100)!(  1, 51)(  2, 55)(  3, 54)(  4, 53)(  5, 52)(  6, 71)(  7, 75)(  8, 74)(  9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)( 16, 61)( 17, 65)( 18, 64)( 19, 63)( 20, 62)( 21, 56)( 22, 60)( 23, 59)( 24, 58)( 25, 57)( 26, 76)( 27, 80)( 28, 79)( 29, 78)( 30, 77)( 31, 96)( 32,100)( 33, 99)( 34, 98)( 35, 97)( 36, 91)( 37, 95)( 38, 94)( 39, 93)( 40, 92)( 41, 86)( 42, 90)( 43, 89)( 44, 88)( 45, 87)( 46, 81)( 47, 85)( 48, 84)( 49, 83)( 50, 82);
s1 := Sym(100)!(  1, 12)(  2, 24)(  3,  6)(  4, 18)(  7, 15)(  8, 22)( 10, 16)( 11, 19)( 14, 25)( 20, 23)( 26, 37)( 27, 49)( 28, 31)( 29, 43)( 32, 40)( 33, 47)( 35, 41)( 36, 44)( 39, 50)( 45, 48)( 51, 87)( 52, 99)( 53, 81)( 54, 93)( 55, 80)( 56, 78)( 57, 90)( 58, 97)( 59, 84)( 60, 91)( 61, 94)( 62, 76)( 63, 88)( 64,100)( 65, 82)( 66, 85)( 67, 92)( 68, 79)( 69, 86)( 70, 98)( 71, 96)( 72, 83)( 73, 95)( 74, 77)( 75, 89);
s2 := Sym(100)!(  2,  7)(  3, 13)(  4, 19)(  5, 25)(  6, 21)(  9, 14)( 10, 20)( 11, 16)( 12, 22)( 18, 23)( 27, 32)( 28, 38)( 29, 44)( 30, 50)( 31, 46)( 34, 39)( 35, 45)( 36, 41)( 37, 47)( 43, 48)( 52, 57)( 53, 63)( 54, 69)( 55, 75)( 56, 71)( 59, 64)( 60, 70)( 61, 66)( 62, 72)( 68, 73)( 77, 82)( 78, 88)( 79, 94)( 80,100)( 81, 96)( 84, 89)( 85, 95)( 86, 91)( 87, 97)( 93, 98);
poly := sub<Sym(100)|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, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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*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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;

References

None.

to this polytope.

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