Polytope of Type {2,100,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,100,2}*800
if this polytope has a name.
Group : SmallGroup(800,218)
Rank : 4
Schlafli Type : {2,100,2}
Number of vertices, edges, etc : 2, 100, 100, 2
Order of s₀s₁s₂s₃ : 100
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,100,2,2} of size 1600
Vertex Figure Of :
   {2,2,100,2} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,50,2}*400
   4-fold quotients : {2,25,2}*200
   5-fold quotients : {2,20,2}*160
   10-fold quotients : {2,10,2}*80
   20-fold quotients : {2,5,2}*40
   25-fold quotients : {2,4,2}*32
   50-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,100,4}*1600, {4,100,2}*1600, {2,200,2}*1600
Permutation Representation (GAP) :

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

to this polytope