Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,10}

Atlas Canonical Name {10,10}*1000d

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1000,183)
Rank
3
Schläfli Type
{10,10}
Vertices, edges, …
50, 250, 50
Order of s0s1s2
10
Order of s0s1s2s1
10
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Self-Dual
  • Self-Petrie

Quotients maximal quotients in bold

5-fold

10-fold

25-fold

50-fold

125-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> of order 2

30 facets

25 vertex figures

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

25 facets

30 vertex figures

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

10 facets

10 vertex figures

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

30 facets

10 vertex figures

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

10 facets

10 vertex figures

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

10 facets

10 vertex figures

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

10 facets

10 vertex figures

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

10 facets

30 vertex figures

Representations

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