Polytope of Type {2,126}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,126}*504
if this polytope has a name.
Group : SmallGroup(504,65)
Rank : 3
Schlafli Type : {2,126}
Number of vertices, edges, etc : 2, 126, 126
Order of s₀s₁s₂ : 126
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,126,2} of size 1008
Vertex Figure Of :
   {2,2,126} of size 1008
   {3,2,126} of size 1512
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,63}*252
   3-fold quotients : {2,42}*168
   6-fold quotients : {2,21}*84
   7-fold quotients : {2,18}*72
   9-fold quotients : {2,14}*56
   14-fold quotients : {2,9}*36
   18-fold quotients : {2,7}*28
   21-fold quotients : {2,6}*24
   42-fold quotients : {2,3}*12
   63-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,252}*1008, {4,126}*1008a
   3-fold covers : {2,378}*1512, {6,126}*1512a, {6,126}*1512b
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  6, 21)(  7, 23)(  8, 22)(  9, 18)( 10, 20)( 11, 19)( 12, 15)
( 13, 17)( 14, 16)( 24, 46)( 25, 45)( 26, 47)( 27, 64)( 28, 63)( 29, 65)
( 30, 61)( 31, 60)( 32, 62)( 33, 58)( 34, 57)( 35, 59)( 36, 55)( 37, 54)
( 38, 56)( 39, 52)( 40, 51)( 41, 53)( 42, 49)( 43, 48)( 44, 50)( 67, 68)
( 69, 84)( 70, 86)( 71, 85)( 72, 81)( 73, 83)( 74, 82)( 75, 78)( 76, 80)
( 77, 79)( 87,109)( 88,108)( 89,110)( 90,127)( 91,126)( 92,128)( 93,124)
( 94,123)( 95,125)( 96,121)( 97,120)( 98,122)( 99,118)(100,117)(101,119)
(102,115)(103,114)(104,116)(105,112)(106,111)(107,113);;
s2 := (  3, 90)(  4, 92)(  5, 91)(  6, 87)(  7, 89)(  8, 88)(  9,105)( 10,107)
( 11,106)( 12,102)( 13,104)( 14,103)( 15, 99)( 16,101)( 17,100)( 18, 96)
( 19, 98)( 20, 97)( 21, 93)( 22, 95)( 23, 94)( 24, 69)( 25, 71)( 26, 70)
( 27, 66)( 28, 68)( 29, 67)( 30, 84)( 31, 86)( 32, 85)( 33, 81)( 34, 83)
( 35, 82)( 36, 78)( 37, 80)( 38, 79)( 39, 75)( 40, 77)( 41, 76)( 42, 72)
( 43, 74)( 44, 73)( 45,112)( 46,111)( 47,113)( 48,109)( 49,108)( 50,110)
( 51,127)( 52,126)( 53,128)( 54,124)( 55,123)( 56,125)( 57,121)( 58,120)
( 59,122)( 60,118)( 61,117)( 62,119)( 63,115)( 64,114)( 65,116);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(128)!(1,2);
s1 := Sym(128)!(  4,  5)(  6, 21)(  7, 23)(  8, 22)(  9, 18)( 10, 20)( 11, 19)
( 12, 15)( 13, 17)( 14, 16)( 24, 46)( 25, 45)( 26, 47)( 27, 64)( 28, 63)
( 29, 65)( 30, 61)( 31, 60)( 32, 62)( 33, 58)( 34, 57)( 35, 59)( 36, 55)
( 37, 54)( 38, 56)( 39, 52)( 40, 51)( 41, 53)( 42, 49)( 43, 48)( 44, 50)
( 67, 68)( 69, 84)( 70, 86)( 71, 85)( 72, 81)( 73, 83)( 74, 82)( 75, 78)
( 76, 80)( 77, 79)( 87,109)( 88,108)( 89,110)( 90,127)( 91,126)( 92,128)
( 93,124)( 94,123)( 95,125)( 96,121)( 97,120)( 98,122)( 99,118)(100,117)
(101,119)(102,115)(103,114)(104,116)(105,112)(106,111)(107,113);
s2 := Sym(128)!(  3, 90)(  4, 92)(  5, 91)(  6, 87)(  7, 89)(  8, 88)(  9,105)
( 10,107)( 11,106)( 12,102)( 13,104)( 14,103)( 15, 99)( 16,101)( 17,100)
( 18, 96)( 19, 98)( 20, 97)( 21, 93)( 22, 95)( 23, 94)( 24, 69)( 25, 71)
( 26, 70)( 27, 66)( 28, 68)( 29, 67)( 30, 84)( 31, 86)( 32, 85)( 33, 81)
( 34, 83)( 35, 82)( 36, 78)( 37, 80)( 38, 79)( 39, 75)( 40, 77)( 41, 76)
( 42, 72)( 43, 74)( 44, 73)( 45,112)( 46,111)( 47,113)( 48,109)( 49,108)
( 50,110)( 51,127)( 52,126)( 53,128)( 54,124)( 55,123)( 56,125)( 57,121)
( 58,120)( 59,122)( 60,118)( 61,117)( 62,119)( 63,115)( 64,114)( 65,116);
poly := sub<Sym(128)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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