Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,52,4}

Atlas Canonical Name {2,52,4}*832

Overview

Group
SmallGroup(832,1158)
Rank
4
Schläfli Type
{2,52,4}
Vertices, edges, …
2, 52, 104, 4
Order of s0s1s2s3
52
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

13-fold

26-fold

52-fold

Covers minimal covers in bold

2-fold

Representations

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