Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,30}

Atlas Canonical Name {10,30}*1500d

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1500,37)
Rank
3
Schläfli Type
{10,30}
Vertices, edges, …
25, 375, 75
Order of s0s1s2
15
Order of s0s1s2s1
10
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

5-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle