Polytope of Type {2,14,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,4}*1568
if this polytope has a name.
Group : SmallGroup(1568,921)
Rank : 4
Schlafli Type : {2,14,4}
Number of vertices, edges, etc : 2, 98, 196, 28
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,14,4}*784
   49-fold quotients : {2,2,4}*32
   98-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope