Polytope of Type {2,4,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,14}*1568
if this polytope has a name.
Group : SmallGroup(1568,921)
Rank : 4
Schlafli Type : {2,4,14}
Number of vertices, edges, etc : 2, 28, 196, 98
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 : {2,4,14}*784
   49-fold quotients : {2,4,2}*32
   98-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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, 95)
( 11, 94)( 12,100)( 13, 99)( 14, 98)( 15, 97)( 16, 96)( 17, 88)( 18, 87)
( 19, 93)( 20, 92)( 21, 91)( 22, 90)( 23, 89)( 24, 81)( 25, 80)( 26, 86)
( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 74)( 32, 73)( 33, 79)( 34, 78)
( 35, 77)( 36, 76)( 37, 75)( 38, 67)( 39, 66)( 40, 72)( 41, 71)( 42, 70)
( 43, 69)( 44, 68)( 45, 60)( 46, 59)( 47, 65)( 48, 64)( 49, 63)( 50, 62)
( 51, 61);;
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, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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, 95)( 11, 94)( 12,100)( 13, 99)( 14, 98)( 15, 97)( 16, 96)( 17, 88)
( 18, 87)( 19, 93)( 20, 92)( 21, 91)( 22, 90)( 23, 89)( 24, 81)( 25, 80)
( 26, 86)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 74)( 32, 73)( 33, 79)
( 34, 78)( 35, 77)( 36, 76)( 37, 75)( 38, 67)( 39, 66)( 40, 72)( 41, 71)
( 42, 70)( 43, 69)( 44, 68)( 45, 60)( 46, 59)( 47, 65)( 48, 64)( 49, 63)
( 50, 62)( 51, 61);
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, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope