Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,10}

Atlas Canonical Name {6,10}*1500a

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1500,37)
Rank
3
Schläfli Type
{6,10}
Vertices, edges, …
75, 375, 125
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 := (  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 := (  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 26, 41)( 27, 45)( 28, 44)( 29, 43)( 30, 42)( 31, 36)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 50)( 48, 49)( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 72)( 62, 71)( 63, 75)( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76, 99)( 77, 98)( 78, 97)( 79, 96)( 80,100)( 81, 94)( 82, 93)( 83, 92)( 84, 91)( 85, 95)( 86, 89)( 87, 88)(101,112)(102,111)(103,115)(104,114)(105,113)(106,107)(108,110)(116,122)(117,121)(118,125)(119,124)(120,123);;
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*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0 ];;
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)!(  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 26, 41)( 27, 45)( 28, 44)( 29, 43)( 30, 42)( 31, 36)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 50)( 48, 49)( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 72)( 62, 71)( 63, 75)( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76, 99)( 77, 98)( 78, 97)( 79, 96)( 80,100)( 81, 94)( 82, 93)( 83, 92)( 84, 91)( 85, 95)( 86, 89)( 87, 88)(101,112)(102,111)(103,115)(104,114)(105,113)(106,107)(108,110)(116,122)(117,121)(118,125)(119,124)(120,123);
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*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0 >;

References

None.

to this polytope.

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