Polytope of Type {2,15,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,15,2}*120
if this polytope has a name.
Group : SmallGroup(120,46)
Rank : 4
Schlafli Type : {2,15,2}
Number of vertices, edges, etc : 2, 15, 15, 2
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,15,2,2} of size 240
{2,15,2,3} of size 360
{2,15,2,4} of size 480
{2,15,2,5} of size 600
{2,15,2,6} of size 720
{2,15,2,7} of size 840
{2,15,2,8} of size 960
{2,15,2,9} of size 1080
{2,15,2,10} of size 1200
{2,15,2,11} of size 1320
{2,15,2,12} of size 1440
{2,15,2,13} of size 1560
{2,15,2,14} of size 1680
{2,15,2,15} of size 1800
{2,15,2,16} of size 1920
Vertex Figure Of :
{2,2,15,2} of size 240
{3,2,15,2} of size 360
{4,2,15,2} of size 480
{5,2,15,2} of size 600
{6,2,15,2} of size 720
{7,2,15,2} of size 840
{8,2,15,2} of size 960
{9,2,15,2} of size 1080
{10,2,15,2} of size 1200
{11,2,15,2} of size 1320
{12,2,15,2} of size 1440
{13,2,15,2} of size 1560
{14,2,15,2} of size 1680
{15,2,15,2} of size 1800
{16,2,15,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,5,2}*40
5-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,30,2}*240
3-fold covers : {2,45,2}*360, {2,15,6}*360, {6,15,2}*360
4-fold covers : {2,60,2}*480, {2,30,4}*480a, {4,30,2}*480a, {2,15,4}*480, {4,15,2}*480
5-fold covers : {2,75,2}*600, {2,15,10}*600, {10,15,2}*600
6-fold covers : {2,90,2}*720, {2,30,6}*720b, {2,30,6}*720c, {6,30,2}*720b, {6,30,2}*720c
7-fold covers : {2,105,2}*840
8-fold covers : {2,60,4}*960a, {4,60,2}*960a, {4,30,4}*960a, {2,120,2}*960, {2,30,8}*960, {8,30,2}*960, {2,15,8}*960, {8,15,2}*960, {2,30,4}*960, {4,30,2}*960
9-fold covers : {2,135,2}*1080, {2,45,6}*1080, {6,45,2}*1080, {2,15,6}*1080, {6,15,2}*1080, {6,15,6}*1080
10-fold covers : {2,150,2}*1200, {2,30,10}*1200b, {2,30,10}*1200c, {10,30,2}*1200b, {10,30,2}*1200c
11-fold covers : {2,165,2}*1320
12-fold covers : {2,180,2}*1440, {2,90,4}*1440a, {4,90,2}*1440a, {2,45,4}*1440, {4,45,2}*1440, {2,30,12}*1440b, {12,30,2}*1440b, {2,60,6}*1440b, {2,60,6}*1440c, {6,60,2}*1440b, {6,60,2}*1440c, {4,30,6}*1440b, {4,30,6}*1440c, {6,30,4}*1440b, {6,30,4}*1440c, {2,30,12}*1440c, {12,30,2}*1440c, {4,15,6}*1440b, {6,15,4}*1440b, {2,15,12}*1440, {12,15,2}*1440, {2,15,6}*1440e, {6,15,2}*1440e
13-fold covers : {2,195,2}*1560
14-fold covers : {2,30,14}*1680, {14,30,2}*1680, {2,210,2}*1680
15-fold covers : {2,225,2}*1800, {2,75,6}*1800, {6,75,2}*1800, {2,45,10}*1800, {10,45,2}*1800, {6,15,10}*1800, {10,15,6}*1800, {2,15,30}*1800, {30,15,2}*1800
16-fold covers : {4,60,4}*1920a, {2,60,8}*1920a, {8,60,2}*1920a, {2,120,4}*1920a, {4,120,2}*1920a, {2,60,8}*1920b, {8,60,2}*1920b, {2,120,4}*1920b, {4,120,2}*1920b, {2,60,4}*1920a, {4,60,2}*1920a, {4,30,8}*1920a, {8,30,4}*1920a, {2,30,16}*1920, {16,30,2}*1920, {2,240,2}*1920, {2,15,8}*1920a, {8,15,2}*1920a, {2,60,4}*1920b, {4,60,2}*1920b, {4,30,4}*1920a, {4,30,4}*1920b, {2,30,4}*1920b, {2,60,4}*1920c, {4,30,2}*1920b, {4,60,2}*1920c, {2,30,8}*1920b, {8,30,2}*1920b, {2,30,8}*1920c, {8,30,2}*1920c, {2,15,4}*1920, {4,15,2}*1920, {4,15,4}*1920c
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
s3 := (18,19);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*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(19)!(1,2);
s1 := Sym(19)!( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);
s2 := Sym(19)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s3 := Sym(19)!(18,19);
poly := sub<Sym(19)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*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