Polytope of Type {2,2,2,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,10}*160
if this polytope has a name.
Group : SmallGroup(160,237)
Rank : 5
Schlafli Type : {2,2,2,10}
Number of vertices, edges, etc : 2, 2, 2, 10, 10
Order of s0s1s2s3s4 : 10
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,2,10,2} of size 320
{2,2,2,10,4} of size 640
{2,2,2,10,5} of size 800
{2,2,2,10,3} of size 960
{2,2,2,10,3} of size 960
{2,2,2,10,5} of size 960
{2,2,2,10,5} of size 960
{2,2,2,10,6} of size 960
{2,2,2,10,8} of size 1280
{2,2,2,10,4} of size 1600
{2,2,2,10,10} of size 1600
{2,2,2,10,10} of size 1600
{2,2,2,10,10} of size 1600
{2,2,2,10,12} of size 1920
{2,2,2,10,4} of size 1920
{2,2,2,10,4} of size 1920
{2,2,2,10,6} of size 1920
{2,2,2,10,6} of size 1920
{2,2,2,10,3} of size 1920
{2,2,2,10,5} of size 1920
{2,2,2,10,6} of size 1920
{2,2,2,10,6} of size 1920
{2,2,2,10,6} of size 1920
{2,2,2,10,6} of size 1920
{2,2,2,10,10} of size 1920
{2,2,2,10,10} of size 1920
{2,2,2,10,10} of size 1920
{2,2,2,10,10} of size 1920
Vertex Figure Of :
{2,2,2,2,10} of size 320
{3,2,2,2,10} of size 480
{4,2,2,2,10} of size 640
{5,2,2,2,10} of size 800
{6,2,2,2,10} of size 960
{7,2,2,2,10} of size 1120
{8,2,2,2,10} of size 1280
{9,2,2,2,10} of size 1440
{10,2,2,2,10} of size 1600
{11,2,2,2,10} of size 1760
{12,2,2,2,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,2,5}*80
5-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,2,2,20}*320, {2,2,4,10}*320, {2,4,2,10}*320, {4,2,2,10}*320
3-fold covers : {2,2,6,10}*480, {2,6,2,10}*480, {6,2,2,10}*480, {2,2,2,30}*480
4-fold covers : {2,2,4,20}*640, {2,4,2,20}*640, {4,2,2,20}*640, {2,4,4,10}*640, {4,4,2,10}*640, {4,2,4,10}*640, {2,2,2,40}*640, {2,2,8,10}*640, {2,8,2,10}*640, {8,2,2,10}*640
5-fold covers : {2,2,2,50}*800, {2,2,10,10}*800a, {2,2,10,10}*800b, {2,10,2,10}*800, {10,2,2,10}*800
6-fold covers : {2,2,12,10}*960, {2,12,2,10}*960, {12,2,2,10}*960, {2,2,6,20}*960a, {2,6,2,20}*960, {6,2,2,20}*960, {2,4,6,10}*960a, {2,6,4,10}*960, {4,2,6,10}*960, {4,6,2,10}*960a, {6,2,4,10}*960, {6,4,2,10}*960a, {2,2,2,60}*960, {2,2,4,30}*960a, {2,4,2,30}*960, {4,2,2,30}*960
7-fold covers : {2,2,14,10}*1120, {2,14,2,10}*1120, {14,2,2,10}*1120, {2,2,2,70}*1120
8-fold covers : {4,4,4,10}*1280, {2,4,4,20}*1280, {4,4,2,20}*1280, {4,2,4,20}*1280, {2,4,8,10}*1280a, {2,8,4,10}*1280a, {4,8,2,10}*1280a, {8,4,2,10}*1280a, {2,2,8,20}*1280a, {2,2,4,40}*1280a, {2,4,8,10}*1280b, {2,8,4,10}*1280b, {4,8,2,10}*1280b, {8,4,2,10}*1280b, {2,2,8,20}*1280b, {2,2,4,40}*1280b, {2,4,4,10}*1280, {4,4,2,10}*1280, {2,2,4,20}*1280, {4,2,8,10}*1280, {8,2,4,10}*1280, {2,8,2,20}*1280, {8,2,2,20}*1280, {2,4,2,40}*1280, {4,2,2,40}*1280, {2,2,16,10}*1280, {2,16,2,10}*1280, {16,2,2,10}*1280, {2,2,2,80}*1280
9-fold covers : {2,2,18,10}*1440, {2,18,2,10}*1440, {18,2,2,10}*1440, {2,2,2,90}*1440, {2,2,6,30}*1440a, {2,6,6,10}*1440a, {2,6,6,10}*1440b, {2,6,6,10}*1440c, {6,2,6,10}*1440, {6,6,2,10}*1440a, {6,6,2,10}*1440b, {6,6,2,10}*1440c, {2,2,6,30}*1440b, {2,2,6,30}*1440c, {2,6,2,30}*1440, {6,2,2,30}*1440
10-fold covers : {2,2,2,100}*1600, {2,2,4,50}*1600, {2,4,2,50}*1600, {4,2,2,50}*1600, {2,2,10,20}*1600a, {2,2,10,20}*1600b, {2,2,20,10}*1600a, {2,10,2,20}*1600, {2,20,2,10}*1600, {10,2,2,20}*1600, {20,2,2,10}*1600, {2,4,10,10}*1600a, {2,10,4,10}*1600, {4,2,10,10}*1600a, {4,2,10,10}*1600b, {4,10,2,10}*1600, {10,2,4,10}*1600, {10,4,2,10}*1600, {2,2,20,10}*1600c, {2,4,10,10}*1600c
11-fold covers : {2,2,22,10}*1760, {2,22,2,10}*1760, {22,2,2,10}*1760, {2,2,2,110}*1760
12-fold covers : {2,4,4,30}*1920, {4,4,2,30}*1920, {2,2,4,60}*1920a, {4,4,6,10}*1920, {6,4,4,10}*1920, {2,4,12,10}*1920a, {2,12,4,10}*1920, {4,12,2,10}*1920a, {12,4,2,10}*1920a, {2,6,4,20}*1920, {6,2,4,20}*1920, {2,2,12,20}*1920, {4,2,4,30}*1920a, {2,4,2,60}*1920, {4,2,2,60}*1920, {4,6,4,10}*1920a, {4,2,12,10}*1920, {12,2,4,10}*1920, {4,2,6,20}*1920a, {4,6,2,20}*1920a, {6,4,2,20}*1920a, {2,4,6,20}*1920a, {2,12,2,20}*1920, {12,2,2,20}*1920, {2,2,8,30}*1920, {2,8,2,30}*1920, {8,2,2,30}*1920, {2,2,2,120}*1920, {2,6,8,10}*1920, {2,8,6,10}*1920, {6,2,8,10}*1920, {6,8,2,10}*1920, {8,2,6,10}*1920, {8,6,2,10}*1920, {2,2,24,10}*1920, {2,24,2,10}*1920, {24,2,2,10}*1920, {2,2,6,40}*1920, {2,6,2,40}*1920, {6,2,2,40}*1920, {2,2,6,20}*1920a, {2,2,6,30}*1920, {2,4,6,10}*1920a, {2,6,4,10}*1920, {2,6,6,10}*1920, {4,6,2,10}*1920, {6,4,2,10}*1920, {6,6,2,10}*1920, {2,2,4,30}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 9,10)(11,12)(13,14)(15,16);;
s4 := ( 7,11)( 8, 9)(10,15)(12,13)(14,16);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(16)!(1,2);
s1 := Sym(16)!(3,4);
s2 := Sym(16)!(5,6);
s3 := Sym(16)!( 9,10)(11,12)(13,14)(15,16);
s4 := Sym(16)!( 7,11)( 8, 9)(10,15)(12,13)(14,16);
poly := sub<Sym(16)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope