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Polytope of Type {102}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {102}*204
Also Known As : 102-gon, {102}. if this polytope has another name.
Group : SmallGroup(204,11)
Rank : 2
Schlafli Type : {102}
Number of vertices, edges, etc : 102, 102
Order of s0s1 : 102
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {102,2} of size 408
   {102,4} of size 816
   {102,4} of size 816
   {102,4} of size 816
   {102,6} of size 1224
   {102,6} of size 1224
   {102,6} of size 1224
   {102,8} of size 1632
   {102,6} of size 1632
   {102,4} of size 1632
   {102,6} of size 1836
Vertex Figure Of :
   {2,102} of size 408
   {4,102} of size 816
   {4,102} of size 816
   {4,102} of size 816
   {6,102} of size 1224
   {6,102} of size 1224
   {6,102} of size 1224
   {8,102} of size 1632
   {6,102} of size 1632
   {4,102} of size 1632
   {6,102} of size 1836
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {51}*102
   3-fold quotients : {34}*68
   6-fold quotients : {17}*34
   17-fold quotients : {6}*12
   34-fold quotients : {3}*6
   51-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {204}*408
   3-fold covers : {306}*612
   4-fold covers : {408}*816
   5-fold covers : {510}*1020
   6-fold covers : {612}*1224
   7-fold covers : {714}*1428
   8-fold covers : {816}*1632
   9-fold covers : {918}*1836
Permutation Representation (GAP) :
s0 := (  2, 17)(  3, 16)(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)
( 18, 35)( 19, 51)( 20, 50)( 21, 49)( 22, 48)( 23, 47)( 24, 46)( 25, 45)
( 26, 44)( 27, 43)( 28, 42)( 29, 41)( 30, 40)( 31, 39)( 32, 38)( 33, 37)
( 34, 36)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)
( 60, 61)( 69, 86)( 70,102)( 71,101)( 72,100)( 73, 99)( 74, 98)( 75, 97)
( 76, 96)( 77, 95)( 78, 94)( 79, 93)( 80, 92)( 81, 91)( 82, 90)( 83, 89)
( 84, 88)( 85, 87);;
s1 := (  1, 70)(  2, 69)(  3, 85)(  4, 84)(  5, 83)(  6, 82)(  7, 81)(  8, 80)
(  9, 79)( 10, 78)( 11, 77)( 12, 76)( 13, 75)( 14, 74)( 15, 73)( 16, 72)
( 17, 71)( 18, 53)( 19, 52)( 20, 68)( 21, 67)( 22, 66)( 23, 65)( 24, 64)
( 25, 63)( 26, 62)( 27, 61)( 28, 60)( 29, 59)( 30, 58)( 31, 57)( 32, 56)
( 33, 55)( 34, 54)( 35, 87)( 36, 86)( 37,102)( 38,101)( 39,100)( 40, 99)
( 41, 98)( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 92)( 48, 91)
( 49, 90)( 50, 89)( 51, 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*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(102)!(  2, 17)(  3, 16)(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)
(  9, 10)( 18, 35)( 19, 51)( 20, 50)( 21, 49)( 22, 48)( 23, 47)( 24, 46)
( 25, 45)( 26, 44)( 27, 43)( 28, 42)( 29, 41)( 30, 40)( 31, 39)( 32, 38)
( 33, 37)( 34, 36)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)
( 59, 62)( 60, 61)( 69, 86)( 70,102)( 71,101)( 72,100)( 73, 99)( 74, 98)
( 75, 97)( 76, 96)( 77, 95)( 78, 94)( 79, 93)( 80, 92)( 81, 91)( 82, 90)
( 83, 89)( 84, 88)( 85, 87);
s1 := Sym(102)!(  1, 70)(  2, 69)(  3, 85)(  4, 84)(  5, 83)(  6, 82)(  7, 81)
(  8, 80)(  9, 79)( 10, 78)( 11, 77)( 12, 76)( 13, 75)( 14, 74)( 15, 73)
( 16, 72)( 17, 71)( 18, 53)( 19, 52)( 20, 68)( 21, 67)( 22, 66)( 23, 65)
( 24, 64)( 25, 63)( 26, 62)( 27, 61)( 28, 60)( 29, 59)( 30, 58)( 31, 57)
( 32, 56)( 33, 55)( 34, 54)( 35, 87)( 36, 86)( 37,102)( 38,101)( 39,100)
( 40, 99)( 41, 98)( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 92)
( 48, 91)( 49, 90)( 50, 89)( 51, 88);
poly := sub<Sym(102)|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*s0*s1*s0*s1 >; 
 
References : None.
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