Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,2,10,10}

Atlas Canonical Name {2,2,2,10,10}*1600c

Overview

Group
SmallGroup(1600,10278)
Rank
6
Schläfli Type
{2,2,2,10,10}
Vertices, edges, …
2, 2, 2, 10, 50, 10
Order of s0s1s2s3s4s5
10
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

5-fold

10-fold

25-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := (  7, 57)(  8, 61)(  9, 60)( 10, 59)( 11, 58)( 12, 77)( 13, 81)( 14, 80)( 15, 79)( 16, 78)( 17, 72)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 67)( 23, 71)( 24, 70)( 25, 69)( 26, 68)( 27, 62)( 28, 66)( 29, 65)( 30, 64)( 31, 63)( 32, 82)( 33, 86)( 34, 85)( 35, 84)( 36, 83)( 37,102)( 38,106)( 39,105)( 40,104)( 41,103)( 42, 97)( 43,101)( 44,100)( 45, 99)( 46, 98)( 47, 92)( 48, 96)( 49, 95)( 50, 94)( 51, 93)( 52, 87)( 53, 91)( 54, 90)( 55, 89)( 56, 88);;
s4 := (  7, 88)(  8, 87)(  9, 91)( 10, 90)( 11, 89)( 12, 83)( 13, 82)( 14, 86)( 15, 85)( 16, 84)( 17,103)( 18,102)( 19,106)( 20,105)( 21,104)( 22, 98)( 23, 97)( 24,101)( 25,100)( 26, 99)( 27, 93)( 28, 92)( 29, 96)( 30, 95)( 31, 94)( 32, 63)( 33, 62)( 34, 66)( 35, 65)( 36, 64)( 37, 58)( 38, 57)( 39, 61)( 40, 60)( 41, 59)( 42, 78)( 43, 77)( 44, 81)( 45, 80)( 46, 79)( 47, 73)( 48, 72)( 49, 76)( 50, 75)( 51, 74)( 52, 68)( 53, 67)( 54, 71)( 55, 70)( 56, 69);;
s5 := (  8, 11)(  9, 10)( 13, 16)( 14, 15)( 18, 21)( 19, 20)( 23, 26)( 24, 25)( 28, 31)( 29, 30)( 33, 36)( 34, 35)( 38, 41)( 39, 40)( 43, 46)( 44, 45)( 48, 51)( 49, 50)( 53, 56)( 54, 55)( 58, 61)( 59, 60)( 63, 66)( 64, 65)( 68, 71)( 69, 70)( 73, 76)( 74, 75)( 78, 81)( 79, 80)( 83, 86)( 84, 85)( 88, 91)( 89, 90)( 93, 96)( 94, 95)( 98,101)( 99,100)(103,106)(104,105);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s5*s4*s3*s4*s3*s4*s3*s4*s3*s4*s5*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(106)!(1,2);
s1 := Sym(106)!(3,4);
s2 := Sym(106)!(5,6);
s3 := Sym(106)!(  7, 57)(  8, 61)(  9, 60)( 10, 59)( 11, 58)( 12, 77)( 13, 81)( 14, 80)( 15, 79)( 16, 78)( 17, 72)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 67)( 23, 71)( 24, 70)( 25, 69)( 26, 68)( 27, 62)( 28, 66)( 29, 65)( 30, 64)( 31, 63)( 32, 82)( 33, 86)( 34, 85)( 35, 84)( 36, 83)( 37,102)( 38,106)( 39,105)( 40,104)( 41,103)( 42, 97)( 43,101)( 44,100)( 45, 99)( 46, 98)( 47, 92)( 48, 96)( 49, 95)( 50, 94)( 51, 93)( 52, 87)( 53, 91)( 54, 90)( 55, 89)( 56, 88);
s4 := Sym(106)!(  7, 88)(  8, 87)(  9, 91)( 10, 90)( 11, 89)( 12, 83)( 13, 82)( 14, 86)( 15, 85)( 16, 84)( 17,103)( 18,102)( 19,106)( 20,105)( 21,104)( 22, 98)( 23, 97)( 24,101)( 25,100)( 26, 99)( 27, 93)( 28, 92)( 29, 96)( 30, 95)( 31, 94)( 32, 63)( 33, 62)( 34, 66)( 35, 65)( 36, 64)( 37, 58)( 38, 57)( 39, 61)( 40, 60)( 41, 59)( 42, 78)( 43, 77)( 44, 81)( 45, 80)( 46, 79)( 47, 73)( 48, 72)( 49, 76)( 50, 75)( 51, 74)( 52, 68)( 53, 67)( 54, 71)( 55, 70)( 56, 69);
s5 := Sym(106)!(  8, 11)(  9, 10)( 13, 16)( 14, 15)( 18, 21)( 19, 20)( 23, 26)( 24, 25)( 28, 31)( 29, 30)( 33, 36)( 34, 35)( 38, 41)( 39, 40)( 43, 46)( 44, 45)( 48, 51)( 49, 50)( 53, 56)( 54, 55)( 58, 61)( 59, 60)( 63, 66)( 64, 65)( 68, 71)( 69, 70)( 73, 76)( 74, 75)( 78, 81)( 79, 80)( 83, 86)( 84, 85)( 88, 91)( 89, 90)( 93, 96)( 94, 95)( 98,101)( 99,100)(103,106)(104,105);
poly := sub<Sym(106)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s5*s4*s3*s4*s3*s4*s3*s4*s3*s4*s5*s4 >;