Polytope of Type {2,102}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,102}*408
if this polytope has a name.
Group : SmallGroup(408,45)
Rank : 3
Schlafli Type : {2,102}
Number of vertices, edges, etc : 2, 102, 102
Order of s₀s₁s₂ : 102
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,102,2} of size 816
   {2,102,4} of size 1632
   {2,102,4} of size 1632
   {2,102,4} of size 1632
Vertex Figure Of :
   {2,2,102} of size 816
   {3,2,102} of size 1224
   {4,2,102} of size 1632
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,51}*204
   3-fold quotients : {2,34}*136
   6-fold quotients : {2,17}*68
   17-fold quotients : {2,6}*24
   34-fold quotients : {2,3}*12
   51-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,204}*816, {4,102}*816a
   3-fold covers : {2,306}*1224, {6,102}*1224b, {6,102}*1224c
   4-fold covers : {4,204}*1632a, {2,408}*1632, {8,102}*1632, {4,102}*1632
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*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*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*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*s1*s2*s1*s2*s1*s2 >;

to this polytope