Polytope of Type {5,2,2,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,2,2,2}*160
if this polytope has a name.
Group : SmallGroup(160,237)
Rank : 6
Schlafli Type : {5,2,2,2,2}
Number of vertices, edges, etc : 5, 5, 2, 2, 2, 2
Order of s0s1s2s3s4s5 : 10
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{5,2,2,2,2,2} of size 320
{5,2,2,2,2,3} of size 480
{5,2,2,2,2,4} of size 640
{5,2,2,2,2,5} of size 800
{5,2,2,2,2,6} of size 960
{5,2,2,2,2,7} of size 1120
{5,2,2,2,2,8} of size 1280
{5,2,2,2,2,9} of size 1440
{5,2,2,2,2,10} of size 1600
{5,2,2,2,2,11} of size 1760
{5,2,2,2,2,12} of size 1920
Vertex Figure Of :
{2,5,2,2,2,2} of size 320
{3,5,2,2,2,2} of size 960
{5,5,2,2,2,2} of size 960
{10,5,2,2,2,2} of size 1600
{4,5,2,2,2,2} of size 1920
{6,5,2,2,2,2} of size 1920
{3,5,2,2,2,2} of size 1920
{5,5,2,2,2,2} of size 1920
{6,5,2,2,2,2} of size 1920
{6,5,2,2,2,2} of size 1920
{10,5,2,2,2,2} of size 1920
{10,5,2,2,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,2,2,2,4}*320, {5,2,2,4,2}*320, {5,2,4,2,2}*320, {10,2,2,2,2}*320
3-fold covers : {5,2,2,2,6}*480, {5,2,2,6,2}*480, {5,2,6,2,2}*480, {15,2,2,2,2}*480
4-fold covers : {5,2,2,4,4}*640, {5,2,4,4,2}*640, {5,2,4,2,4}*640, {5,2,2,2,8}*640, {5,2,2,8,2}*640, {5,2,8,2,2}*640, {20,2,2,2,2}*640, {10,2,2,2,4}*640, {10,2,2,4,2}*640, {10,2,4,2,2}*640, {10,4,2,2,2}*640
5-fold covers : {25,2,2,2,2}*800, {5,2,2,2,10}*800, {5,2,2,10,2}*800, {5,2,10,2,2}*800, {5,10,2,2,2}*800
6-fold covers : {5,2,2,2,12}*960, {5,2,2,12,2}*960, {5,2,12,2,2}*960, {5,2,2,4,6}*960a, {5,2,2,6,4}*960a, {5,2,4,2,6}*960, {5,2,4,6,2}*960a, {5,2,6,2,4}*960, {5,2,6,4,2}*960a, {15,2,2,2,4}*960, {15,2,2,4,2}*960, {15,2,4,2,2}*960, {10,2,2,2,6}*960, {10,2,2,6,2}*960, {10,2,6,2,2}*960, {10,6,2,2,2}*960, {30,2,2,2,2}*960
7-fold covers : {5,2,2,2,14}*1120, {5,2,2,14,2}*1120, {5,2,14,2,2}*1120, {35,2,2,2,2}*1120
8-fold covers : {5,2,4,4,4}*1280, {5,2,2,4,8}*1280a, {5,2,2,8,4}*1280a, {5,2,4,8,2}*1280a, {5,2,8,4,2}*1280a, {5,2,2,4,8}*1280b, {5,2,2,8,4}*1280b, {5,2,4,8,2}*1280b, {5,2,8,4,2}*1280b, {5,2,2,4,4}*1280, {5,2,4,4,2}*1280, {5,2,4,2,8}*1280, {5,2,8,2,4}*1280, {5,2,2,2,16}*1280, {5,2,2,16,2}*1280, {5,2,16,2,2}*1280, {10,2,2,4,4}*1280, {10,2,4,4,2}*1280, {10,4,4,2,2}*1280, {20,4,2,2,2}*1280, {10,2,4,2,4}*1280, {10,4,2,2,4}*1280, {10,4,2,4,2}*1280, {20,2,2,2,4}*1280, {20,2,2,4,2}*1280, {20,2,4,2,2}*1280, {10,2,2,2,8}*1280, {10,2,2,8,2}*1280, {10,2,8,2,2}*1280, {10,8,2,2,2}*1280, {40,2,2,2,2}*1280
9-fold covers : {5,2,2,2,18}*1440, {5,2,2,18,2}*1440, {5,2,18,2,2}*1440, {45,2,2,2,2}*1440, {5,2,2,6,6}*1440a, {5,2,2,6,6}*1440b, {5,2,2,6,6}*1440c, {5,2,6,2,6}*1440, {5,2,6,6,2}*1440a, {5,2,6,6,2}*1440b, {5,2,6,6,2}*1440c, {15,2,2,2,6}*1440, {15,2,2,6,2}*1440, {15,2,6,2,2}*1440, {15,6,2,2,2}*1440
10-fold covers : {25,2,2,2,4}*1600, {25,2,2,4,2}*1600, {25,2,4,2,2}*1600, {50,2,2,2,2}*1600, {5,2,2,2,20}*1600, {5,2,2,20,2}*1600, {5,2,20,2,2}*1600, {5,2,2,4,10}*1600, {5,2,2,10,4}*1600, {5,2,4,2,10}*1600, {5,2,4,10,2}*1600, {5,2,10,2,4}*1600, {5,2,10,4,2}*1600, {5,10,2,2,4}*1600, {5,10,2,4,2}*1600, {5,10,4,2,2}*1600, {10,2,2,2,10}*1600, {10,2,2,10,2}*1600, {10,2,10,2,2}*1600, {10,10,2,2,2}*1600a, {10,10,2,2,2}*1600c
11-fold covers : {5,2,2,2,22}*1760, {5,2,2,22,2}*1760, {5,2,22,2,2}*1760, {55,2,2,2,2}*1760
12-fold covers : {15,2,2,4,4}*1920, {15,2,4,4,2}*1920, {5,2,4,4,6}*1920, {5,2,6,4,4}*1920, {5,2,2,4,12}*1920a, {5,2,2,12,4}*1920a, {5,2,4,12,2}*1920a, {5,2,12,4,2}*1920a, {15,2,4,2,4}*1920, {5,2,4,6,4}*1920a, {5,2,4,2,12}*1920, {5,2,12,2,4}*1920, {15,2,2,2,8}*1920, {15,2,2,8,2}*1920, {15,2,8,2,2}*1920, {5,2,2,6,8}*1920, {5,2,2,8,6}*1920, {5,2,6,2,8}*1920, {5,2,6,8,2}*1920, {5,2,8,2,6}*1920, {5,2,8,6,2}*1920, {5,2,2,2,24}*1920, {5,2,2,24,2}*1920, {5,2,24,2,2}*1920, {30,2,2,2,4}*1920, {30,2,2,4,2}*1920, {30,2,4,2,2}*1920, {30,4,2,2,2}*1920a, {60,2,2,2,2}*1920, {10,2,2,4,6}*1920a, {10,2,2,6,4}*1920a, {10,2,4,2,6}*1920, {10,2,4,6,2}*1920a, {10,2,6,2,4}*1920, {10,2,6,4,2}*1920a, {10,4,2,2,6}*1920, {10,4,2,6,2}*1920, {10,4,6,2,2}*1920, {10,6,2,2,4}*1920, {10,6,2,4,2}*1920, {10,6,4,2,2}*1920a, {10,2,2,2,12}*1920, {10,2,2,12,2}*1920, {10,2,12,2,2}*1920, {10,12,2,2,2}*1920, {20,2,2,2,6}*1920, {20,2,2,6,2}*1920, {20,2,6,2,2}*1920, {20,6,2,2,2}*1920a, {5,2,2,4,6}*1920, {5,2,2,6,4}*1920, {5,2,2,6,6}*1920, {5,2,4,6,2}*1920, {5,2,6,4,2}*1920, {5,2,6,6,2}*1920, {15,6,2,2,2}*1920, {15,4,2,2,2}*1920
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (6,7);;
s3 := (8,9);;
s4 := (10,11);;
s5 := (12,13);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(13)!(2,3)(4,5);
s1 := Sym(13)!(1,2)(3,4);
s2 := Sym(13)!(6,7);
s3 := Sym(13)!(8,9);
s4 := Sym(13)!(10,11);
s5 := Sym(13)!(12,13);
poly := sub<Sym(13)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope