Polytope of Type {100}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {100}*200
Also Known As : 100-gon, {100}. if this polytope has another name.
Group : SmallGroup(200,6)
Rank : 2
Schlafli Type : {100}
Number of vertices, edges, etc : 100, 100
Order of s0s1 : 100
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {100,2} of size 400
   {100,4} of size 800
   {100,6} of size 1200
   {100,6} of size 1200
   {100,4} of size 1600
   {100,8} of size 1600
   {100,8} of size 1600
   {100,6} of size 1800
   {100,10} of size 2000
   {100,10} of size 2000
Vertex Figure Of :
   {2,100} of size 400
   {4,100} of size 800
   {6,100} of size 1200
   {6,100} of size 1200
   {4,100} of size 1600
   {8,100} of size 1600
   {8,100} of size 1600
   {6,100} of size 1800
   {10,100} of size 2000
   {10,100} of size 2000
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {50}*100
   4-fold quotients : {25}*50
   5-fold quotients : {20}*40
   10-fold quotients : {10}*20
   20-fold quotients : {5}*10
   25-fold quotients : {4}*8
   50-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {200}*400
   3-fold covers : {300}*600
   4-fold covers : {400}*800
   5-fold covers : {500}*1000
   6-fold covers : {600}*1200
   7-fold covers : {700}*1400
   8-fold covers : {800}*1600
   9-fold covers : {900}*1800
   10-fold covers : {1000}*2000
Permutation Representation (GAP) :
s0 := (  2,  5)(  3,  4)(  6, 22)(  7, 21)(  8, 25)(  9, 24)( 10, 23)( 11, 17)
( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 27, 30)( 28, 29)( 31, 47)( 32, 46)
( 33, 50)( 34, 49)( 35, 48)( 36, 42)( 37, 41)( 38, 45)( 39, 44)( 40, 43)
( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56, 97)( 57, 96)( 58,100)
( 59, 99)( 60, 98)( 61, 92)( 62, 91)( 63, 95)( 64, 94)( 65, 93)( 66, 87)
( 67, 86)( 68, 90)( 69, 89)( 70, 88)( 71, 82)( 72, 81)( 73, 85)( 74, 84)
( 75, 83);;
s1 := (  1, 56)(  2, 60)(  3, 59)(  4, 58)(  5, 57)(  6, 51)(  7, 55)(  8, 54)
(  9, 53)( 10, 52)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)( 16, 67)
( 17, 66)( 18, 70)( 19, 69)( 20, 68)( 21, 62)( 22, 61)( 23, 65)( 24, 64)
( 25, 63)( 26, 81)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 76)( 32, 80)
( 33, 79)( 34, 78)( 35, 77)( 36, 97)( 37, 96)( 38,100)( 39, 99)( 40, 98)
( 41, 92)( 42, 91)( 43, 95)( 44, 94)( 45, 93)( 46, 87)( 47, 86)( 48, 90)
( 49, 89)( 50, 88);;
poly := Group([s0,s1]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(100)!(  2,  5)(  3,  4)(  6, 22)(  7, 21)(  8, 25)(  9, 24)( 10, 23)
( 11, 17)( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 27, 30)( 28, 29)( 31, 47)
( 32, 46)( 33, 50)( 34, 49)( 35, 48)( 36, 42)( 37, 41)( 38, 45)( 39, 44)
( 40, 43)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56, 97)( 57, 96)
( 58,100)( 59, 99)( 60, 98)( 61, 92)( 62, 91)( 63, 95)( 64, 94)( 65, 93)
( 66, 87)( 67, 86)( 68, 90)( 69, 89)( 70, 88)( 71, 82)( 72, 81)( 73, 85)
( 74, 84)( 75, 83);
s1 := Sym(100)!(  1, 56)(  2, 60)(  3, 59)(  4, 58)(  5, 57)(  6, 51)(  7, 55)
(  8, 54)(  9, 53)( 10, 52)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)
( 16, 67)( 17, 66)( 18, 70)( 19, 69)( 20, 68)( 21, 62)( 22, 61)( 23, 65)
( 24, 64)( 25, 63)( 26, 81)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 76)
( 32, 80)( 33, 79)( 34, 78)( 35, 77)( 36, 97)( 37, 96)( 38,100)( 39, 99)
( 40, 98)( 41, 92)( 42, 91)( 43, 95)( 44, 94)( 45, 93)( 46, 87)( 47, 86)
( 48, 90)( 49, 89)( 50, 88);
poly := sub<Sym(100)|s0,s1>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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