Polytope of Type {2,2,2,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,5}*80
if this polytope has a name.
Group : SmallGroup(80,51)
Rank : 5
Schlafli Type : {2,2,2,5}
Number of vertices, edges, etc : 2, 2, 2, 5, 5
Order of s0s1s2s3s4 : 10
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,2,5,2} of size 160
{2,2,2,5,3} of size 480
{2,2,2,5,5} of size 480
{2,2,2,5,10} of size 800
{2,2,2,5,4} of size 960
{2,2,2,5,6} of size 960
{2,2,2,5,3} of size 960
{2,2,2,5,5} of size 960
{2,2,2,5,6} of size 960
{2,2,2,5,6} of size 960
{2,2,2,5,10} of size 960
{2,2,2,5,10} of size 960
{2,2,2,5,4} of size 1280
{2,2,2,5,5} of size 1280
{2,2,2,5,4} of size 1920
{2,2,2,5,6} of size 1920
{2,2,2,5,6} of size 1920
{2,2,2,5,10} of size 1920
Vertex Figure Of :
{2,2,2,2,5} of size 160
{3,2,2,2,5} of size 240
{4,2,2,2,5} of size 320
{5,2,2,2,5} of size 400
{6,2,2,2,5} of size 480
{7,2,2,2,5} of size 560
{8,2,2,2,5} of size 640
{9,2,2,2,5} of size 720
{10,2,2,2,5} of size 800
{11,2,2,2,5} of size 880
{12,2,2,2,5} of size 960
{13,2,2,2,5} of size 1040
{14,2,2,2,5} of size 1120
{15,2,2,2,5} of size 1200
{16,2,2,2,5} of size 1280
{17,2,2,2,5} of size 1360
{18,2,2,2,5} of size 1440
{19,2,2,2,5} of size 1520
{20,2,2,2,5} of size 1600
{21,2,2,2,5} of size 1680
{22,2,2,2,5} of size 1760
{23,2,2,2,5} of size 1840
{24,2,2,2,5} of size 1920
{25,2,2,2,5} of size 2000
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,4,2,5}*160, {4,2,2,5}*160, {2,2,2,10}*160
3-fold covers : {2,6,2,5}*240, {6,2,2,5}*240, {2,2,2,15}*240
4-fold covers : {4,4,2,5}*320, {2,8,2,5}*320, {8,2,2,5}*320, {2,2,2,20}*320, {2,2,4,10}*320, {2,4,2,10}*320, {4,2,2,10}*320
5-fold covers : {2,2,2,25}*400, {2,2,10,5}*400, {2,10,2,5}*400, {10,2,2,5}*400
6-fold covers : {2,12,2,5}*480, {12,2,2,5}*480, {4,6,2,5}*480a, {6,4,2,5}*480a, {2,4,2,15}*480, {4,2,2,15}*480, {2,2,6,10}*480, {2,6,2,10}*480, {6,2,2,10}*480, {2,2,2,30}*480
7-fold covers : {2,14,2,5}*560, {14,2,2,5}*560, {2,2,2,35}*560
8-fold covers : {4,8,2,5}*640a, {8,4,2,5}*640a, {4,8,2,5}*640b, {8,4,2,5}*640b, {4,4,2,5}*640, {2,16,2,5}*640, {16,2,2,5}*640, {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
9-fold covers : {2,18,2,5}*720, {18,2,2,5}*720, {2,2,2,45}*720, {6,6,2,5}*720a, {6,6,2,5}*720b, {6,6,2,5}*720c, {2,2,6,15}*720, {2,6,2,15}*720, {6,2,2,15}*720
10-fold covers : {2,4,2,25}*800, {4,2,2,25}*800, {2,2,2,50}*800, {2,20,2,5}*800, {20,2,2,5}*800, {4,2,10,5}*800, {4,10,2,5}*800, {10,4,2,5}*800, {2,4,10,5}*800, {2,2,10,10}*800a, {2,2,10,10}*800b, {2,10,2,10}*800, {10,2,2,10}*800
11-fold covers : {2,22,2,5}*880, {22,2,2,5}*880, {2,2,2,55}*880
12-fold covers : {4,12,2,5}*960a, {12,4,2,5}*960a, {2,24,2,5}*960, {24,2,2,5}*960, {6,8,2,5}*960, {8,6,2,5}*960, {4,4,2,15}*960, {2,8,2,15}*960, {8,2,2,15}*960, {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, {2,2,6,15}*960, {4,6,2,5}*960, {6,4,2,5}*960, {6,6,2,5}*960, {2,2,4,15}*960
13-fold covers : {2,26,2,5}*1040, {26,2,2,5}*1040, {2,2,2,65}*1040
14-fold covers : {2,28,2,5}*1120, {28,2,2,5}*1120, {4,14,2,5}*1120, {14,4,2,5}*1120, {2,4,2,35}*1120, {4,2,2,35}*1120, {2,2,14,10}*1120, {2,14,2,10}*1120, {14,2,2,10}*1120, {2,2,2,70}*1120
15-fold covers : {2,6,2,25}*1200, {6,2,2,25}*1200, {2,2,2,75}*1200, {2,6,10,5}*1200, {6,2,10,5}*1200, {6,10,2,5}*1200, {10,6,2,5}*1200, {2,2,10,15}*1200, {2,10,2,15}*1200, {2,30,2,5}*1200, {10,2,2,15}*1200, {30,2,2,5}*1200
16-fold covers : {4,8,2,5}*1280a, {8,4,2,5}*1280a, {8,8,2,5}*1280a, {8,8,2,5}*1280b, {8,8,2,5}*1280c, {8,8,2,5}*1280d, {4,16,2,5}*1280a, {16,4,2,5}*1280a, {4,16,2,5}*1280b, {16,4,2,5}*1280b, {4,4,2,5}*1280, {4,8,2,5}*1280b, {8,4,2,5}*1280b, {2,32,2,5}*1280, {32,2,2,5}*1280, {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, {2,2,4,5}*1280
17-fold covers : {2,34,2,5}*1360, {34,2,2,5}*1360, {2,2,2,85}*1360
18-fold covers : {2,36,2,5}*1440, {36,2,2,5}*1440, {4,18,2,5}*1440a, {18,4,2,5}*1440a, {2,4,2,45}*1440, {4,2,2,45}*1440, {2,2,18,10}*1440, {2,18,2,10}*1440, {18,2,2,10}*1440, {2,2,2,90}*1440, {6,12,2,5}*1440a, {6,12,2,5}*1440b, {12,6,2,5}*1440a, {12,6,2,5}*1440b, {6,12,2,5}*1440c, {12,6,2,5}*1440c, {2,12,2,15}*1440, {12,2,2,15}*1440, {4,2,6,15}*1440, {4,6,2,15}*1440a, {6,4,2,15}*1440a, {2,4,6,15}*1440, {4,4,2,5}*1440, {4,6,2,5}*1440, {6,4,2,5}*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
19-fold covers : {2,38,2,5}*1520, {38,2,2,5}*1520, {2,2,2,95}*1520
20-fold covers : {4,4,2,25}*1600, {2,8,2,25}*1600, {8,2,2,25}*1600, {2,2,2,100}*1600, {2,2,4,50}*1600, {2,4,2,50}*1600, {4,2,2,50}*1600, {4,20,2,5}*1600, {20,4,2,5}*1600, {2,40,2,5}*1600, {40,2,2,5}*1600, {8,2,10,5}*1600, {8,10,2,5}*1600, {10,8,2,5}*1600, {2,8,10,5}*1600, {4,4,10,5}*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
21-fold covers : {6,14,2,5}*1680, {14,6,2,5}*1680, {2,14,2,15}*1680, {14,2,2,15}*1680, {2,42,2,5}*1680, {42,2,2,5}*1680, {2,6,2,35}*1680, {6,2,2,35}*1680, {2,2,2,105}*1680
22-fold covers : {2,44,2,5}*1760, {44,2,2,5}*1760, {4,22,2,5}*1760, {22,4,2,5}*1760, {2,4,2,55}*1760, {4,2,2,55}*1760, {2,2,22,10}*1760, {2,22,2,10}*1760, {22,2,2,10}*1760, {2,2,2,110}*1760
23-fold covers : {2,46,2,5}*1840, {46,2,2,5}*1840, {2,2,2,115}*1840
24-fold covers : {4,8,2,15}*1920a, {8,4,2,15}*1920a, {8,12,2,5}*1920a, {12,8,2,5}*1920a, {4,24,2,5}*1920a, {24,4,2,5}*1920a, {4,8,2,15}*1920b, {8,4,2,15}*1920b, {8,12,2,5}*1920b, {12,8,2,5}*1920b, {4,24,2,5}*1920b, {24,4,2,5}*1920b, {4,4,2,15}*1920, {4,12,2,5}*1920a, {12,4,2,5}*1920a, {2,16,2,15}*1920, {16,2,2,15}*1920, {6,16,2,5}*1920, {16,6,2,5}*1920, {2,48,2,5}*1920, {48,2,2,5}*1920, {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, {4,12,2,5}*1920b, {12,4,2,5}*1920b, {4,2,6,15}*1920, {4,6,2,5}*1920b, {4,12,2,5}*1920c, {6,4,2,5}*1920b, {6,12,2,5}*1920a, {12,4,2,5}*1920c, {12,6,2,5}*1920a, {2,2,12,15}*1920, {6,8,2,5}*1920b, {6,12,2,5}*1920b, {8,6,2,5}*1920b, {12,6,2,5}*1920b, {6,6,2,5}*1920b, {6,8,2,5}*1920c, {8,6,2,5}*1920c, {2,4,6,15}*1920, {2,4,4,15}*1920b, {4,2,4,15}*1920, {2,2,8,15}*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
25-fold covers : {2,2,2,125}*2000, {2,2,10,25}*2000, {2,10,2,25}*2000, {2,50,2,5}*2000, {10,2,2,25}*2000, {50,2,2,5}*2000, {2,2,10,5}*2000, {2,10,10,5}*2000a, {2,10,10,5}*2000b, {10,2,10,5}*2000, {10,10,2,5}*2000a, {10,10,2,5}*2000b, {10,10,2,5}*2000c
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 8, 9)(10,11);;
s4 := ( 7, 8)( 9,10);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(11)!(1,2);
s1 := Sym(11)!(3,4);
s2 := Sym(11)!(5,6);
s3 := Sym(11)!( 8, 9)(10,11);
s4 := Sym(11)!( 7, 8)( 9,10);
poly := sub<Sym(11)|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 >;
to this polytope