Part of the Atlas of Small Regular Polytopes

Polytope of Type {20,10}

Atlas Canonical Name {20,10}*2000i

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(2000,919)
Rank
3
Schläfli Type
{20,10}
Vertices, edges, …
100, 500, 50
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

5-fold

10-fold

125-fold

250-fold

Covers minimal covers in bold

None in this atlas.

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)^2*(s2*s1*s0*s1)^4*s2> of order 2

25 facets

50 vertex figures

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

25 facets

55 vertex figures

P/N, where N=<(s0*s1)^2*(s2*s1)^3*s0*s1*s0*s2> of order 5

10 facets

20 vertex figures

P/N, where N=<(s0*s1)^4*(s2*s1*s0*s1)^2> of order 5

10 facets

20 vertex figures

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

10 facets

20 vertex figures

P/N, where N=<(s0*s1*s0*(s2*s1)^3)^2> of order 5

10 facets

20 vertex figures

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

10 facets

20 vertex figures

Representations

Permutation Representation (GAP) 
s0 := (  2,  5)(  3,  4)(  6, 26)(  7, 30)(  8, 29)(  9, 28)( 10, 27)( 11, 51)( 12, 55)( 13, 54)( 14, 53)( 15, 52)( 16, 76)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21,101)( 22,105)( 23,104)( 24,103)( 25,102)( 32, 35)( 33, 34)( 36, 56)( 37, 60)( 38, 59)( 39, 58)( 40, 57)( 41, 81)( 42, 85)( 43, 84)( 44, 83)( 45, 82)( 46,106)( 47,110)( 48,109)( 49,108)( 50,107)( 62, 65)( 63, 64)( 66, 86)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71,111)( 72,115)( 73,114)( 74,113)( 75,112)( 92, 95)( 93, 94)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(122,125)(123,124);;
s1 := (  1,  2)(  3,  5)(  6, 77)(  7, 76)(  8, 80)(  9, 79)( 10, 78)( 11, 27)( 12, 26)( 13, 30)( 14, 29)( 15, 28)( 16,102)( 17,101)( 18,105)( 19,104)( 20,103)( 21, 52)( 22, 51)( 23, 55)( 24, 54)( 25, 53)( 31, 87)( 32, 86)( 33, 90)( 34, 89)( 35, 88)( 36, 37)( 38, 40)( 41,112)( 42,111)( 43,115)( 44,114)( 45,113)( 46, 62)( 47, 61)( 48, 65)( 49, 64)( 50, 63)( 56, 97)( 57, 96)( 58,100)( 59, 99)( 60, 98)( 66,122)( 67,121)( 68,125)( 69,124)( 70,123)( 71, 72)( 73, 75)( 81, 82)( 83, 85)( 91,107)( 92,106)( 93,110)( 94,109)( 95,108)(116,117)(118,120);;
s2 := (  1, 31)(  2, 35)(  3, 34)(  4, 33)(  5, 32)(  6, 26)(  7, 30)(  8, 29)(  9, 28)( 10, 27)( 11, 46)( 12, 50)( 13, 49)( 14, 48)( 15, 47)( 16, 41)( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 36)( 22, 40)( 23, 39)( 24, 38)( 25, 37)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)( 56,101)( 57,105)( 58,104)( 59,103)( 60,102)( 61,121)( 62,125)( 63,124)( 64,123)( 65,122)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 71,111)( 72,115)( 73,114)( 74,113)( 75,112)( 76, 81)( 77, 85)( 78, 84)( 79, 83)( 80, 82)( 86, 96)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 92, 95)( 93, 94);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(125)!(  2,  5)(  3,  4)(  6, 26)(  7, 30)(  8, 29)(  9, 28)( 10, 27)( 11, 51)( 12, 55)( 13, 54)( 14, 53)( 15, 52)( 16, 76)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21,101)( 22,105)( 23,104)( 24,103)( 25,102)( 32, 35)( 33, 34)( 36, 56)( 37, 60)( 38, 59)( 39, 58)( 40, 57)( 41, 81)( 42, 85)( 43, 84)( 44, 83)( 45, 82)( 46,106)( 47,110)( 48,109)( 49,108)( 50,107)( 62, 65)( 63, 64)( 66, 86)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71,111)( 72,115)( 73,114)( 74,113)( 75,112)( 92, 95)( 93, 94)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(122,125)(123,124);
s1 := Sym(125)!(  1,  2)(  3,  5)(  6, 77)(  7, 76)(  8, 80)(  9, 79)( 10, 78)( 11, 27)( 12, 26)( 13, 30)( 14, 29)( 15, 28)( 16,102)( 17,101)( 18,105)( 19,104)( 20,103)( 21, 52)( 22, 51)( 23, 55)( 24, 54)( 25, 53)( 31, 87)( 32, 86)( 33, 90)( 34, 89)( 35, 88)( 36, 37)( 38, 40)( 41,112)( 42,111)( 43,115)( 44,114)( 45,113)( 46, 62)( 47, 61)( 48, 65)( 49, 64)( 50, 63)( 56, 97)( 57, 96)( 58,100)( 59, 99)( 60, 98)( 66,122)( 67,121)( 68,125)( 69,124)( 70,123)( 71, 72)( 73, 75)( 81, 82)( 83, 85)( 91,107)( 92,106)( 93,110)( 94,109)( 95,108)(116,117)(118,120);
s2 := Sym(125)!(  1, 31)(  2, 35)(  3, 34)(  4, 33)(  5, 32)(  6, 26)(  7, 30)(  8, 29)(  9, 28)( 10, 27)( 11, 46)( 12, 50)( 13, 49)( 14, 48)( 15, 47)( 16, 41)( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 36)( 22, 40)( 23, 39)( 24, 38)( 25, 37)( 51,106)( 52,110)( 53,109)( 54,108)( 55,107)( 56,101)( 57,105)( 58,104)( 59,103)( 60,102)( 61,121)( 62,125)( 63,124)( 64,123)( 65,122)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 71,111)( 72,115)( 73,114)( 74,113)( 75,112)( 76, 81)( 77, 85)( 78, 84)( 79, 83)( 80, 82)( 86, 96)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 92, 95)( 93, 94);
poly := sub<Sym(125)|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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.

Twisty Puzzle