Polytope of Type {130}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {130}*260
Also Known As : 130-gon, {130}. if this polytope has another name.
Group : SmallGroup(260,14)
Rank : 2
Schlafli Type : {130}
Number of vertices, edges, etc : 130, 130
Order of s0s1 : 130
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{130,2} of size 520
{130,4} of size 1040
{130,6} of size 1560
Vertex Figure Of :
{2,130} of size 520
{4,130} of size 1040
{6,130} of size 1560
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {65}*130
5-fold quotients : {26}*52
10-fold quotients : {13}*26
13-fold quotients : {10}*20
26-fold quotients : {5}*10
65-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {260}*520
3-fold covers : {390}*780
4-fold covers : {520}*1040
5-fold covers : {650}*1300
6-fold covers : {780}*1560
7-fold covers : {910}*1820
Permutation Representation (GAP) :
s0 := ( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 14, 53)( 15, 65)
( 16, 64)( 17, 63)( 18, 62)( 19, 61)( 20, 60)( 21, 59)( 22, 58)( 23, 57)
( 24, 56)( 25, 55)( 26, 54)( 27, 40)( 28, 52)( 29, 51)( 30, 50)( 31, 49)
( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)( 38, 42)( 39, 41)
( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79,118)( 80,130)
( 81,129)( 82,128)( 83,127)( 84,126)( 85,125)( 86,124)( 87,123)( 88,122)
( 89,121)( 90,120)( 91,119)( 92,105)( 93,117)( 94,116)( 95,115)( 96,114)
( 97,113)( 98,112)( 99,111)(100,110)(101,109)(102,108)(103,107)(104,106);;
s1 := ( 1, 80)( 2, 79)( 3, 91)( 4, 90)( 5, 89)( 6, 88)( 7, 87)( 8, 86)
( 9, 85)( 10, 84)( 11, 83)( 12, 82)( 13, 81)( 14, 67)( 15, 66)( 16, 78)
( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 72)( 23, 71)( 24, 70)
( 25, 69)( 26, 68)( 27,119)( 28,118)( 29,130)( 30,129)( 31,128)( 32,127)
( 33,126)( 34,125)( 35,124)( 36,123)( 37,122)( 38,121)( 39,120)( 40,106)
( 41,105)( 42,117)( 43,116)( 44,115)( 45,114)( 46,113)( 47,112)( 48,111)
( 49,110)( 50,109)( 51,108)( 52,107)( 53, 93)( 54, 92)( 55,104)( 56,103)
( 57,102)( 58,101)( 59,100)( 60, 99)( 61, 98)( 62, 97)( 63, 96)( 64, 95)
( 65, 94);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(130)!( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 14, 53)
( 15, 65)( 16, 64)( 17, 63)( 18, 62)( 19, 61)( 20, 60)( 21, 59)( 22, 58)
( 23, 57)( 24, 56)( 25, 55)( 26, 54)( 27, 40)( 28, 52)( 29, 51)( 30, 50)
( 31, 49)( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)( 38, 42)
( 39, 41)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79,118)
( 80,130)( 81,129)( 82,128)( 83,127)( 84,126)( 85,125)( 86,124)( 87,123)
( 88,122)( 89,121)( 90,120)( 91,119)( 92,105)( 93,117)( 94,116)( 95,115)
( 96,114)( 97,113)( 98,112)( 99,111)(100,110)(101,109)(102,108)(103,107)
(104,106);
s1 := Sym(130)!( 1, 80)( 2, 79)( 3, 91)( 4, 90)( 5, 89)( 6, 88)( 7, 87)
( 8, 86)( 9, 85)( 10, 84)( 11, 83)( 12, 82)( 13, 81)( 14, 67)( 15, 66)
( 16, 78)( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 72)( 23, 71)
( 24, 70)( 25, 69)( 26, 68)( 27,119)( 28,118)( 29,130)( 30,129)( 31,128)
( 32,127)( 33,126)( 34,125)( 35,124)( 36,123)( 37,122)( 38,121)( 39,120)
( 40,106)( 41,105)( 42,117)( 43,116)( 44,115)( 45,114)( 46,113)( 47,112)
( 48,111)( 49,110)( 50,109)( 51,108)( 52,107)( 53, 93)( 54, 92)( 55,104)
( 56,103)( 57,102)( 58,101)( 59,100)( 60, 99)( 61, 98)( 62, 97)( 63, 96)
( 64, 95)( 65, 94);
poly := sub<Sym(130)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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.
to this polytope