Part of the Atlas of Small Regular Polytopes

Polytope of Type {15,10}

Atlas Canonical Name {15,10}*1500c

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