Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,4}

Atlas Canonical Name {2,4,4}*1568

Overview

Group
SmallGroup(1568,921)
Rank
4
Schläfli Type
{2,4,4}
Vertices, edges, …
2, 98, 196, 98
Order of s0s1s2s3
14
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

98-fold

Covers minimal covers in bold

None in this atlas.

Representations

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