Part of the Atlas of Small Regular Polytopes

Polytope of Type {15,10}

Atlas Canonical Name {15,10}*1500d

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1500,37)
Rank
3
Schläfli Type
{15,10}
Vertices, edges, …
75, 375, 50
Order of s0s1s2
30
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

125-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*s2)^2*(s1*s0*s2)^2*s1> of order 5

10 facets

15 vertex figures

Representations

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