Polytope of Type {10,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,2}*80
if this polytope has a name.
Group : SmallGroup(80,51)
Rank : 4
Schlafli Type : {10,2,2}
Number of vertices, edges, etc : 10, 10, 2, 2
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{10,2,2,2} of size 160
{10,2,2,3} of size 240
{10,2,2,4} of size 320
{10,2,2,5} of size 400
{10,2,2,6} of size 480
{10,2,2,7} of size 560
{10,2,2,8} of size 640
{10,2,2,9} of size 720
{10,2,2,10} of size 800
{10,2,2,11} of size 880
{10,2,2,12} of size 960
{10,2,2,13} of size 1040
{10,2,2,14} of size 1120
{10,2,2,15} of size 1200
{10,2,2,16} of size 1280
{10,2,2,17} of size 1360
{10,2,2,18} of size 1440
{10,2,2,19} of size 1520
{10,2,2,20} of size 1600
{10,2,2,21} of size 1680
{10,2,2,22} of size 1760
{10,2,2,23} of size 1840
{10,2,2,24} of size 1920
{10,2,2,25} of size 2000
Vertex Figure Of :
{2,10,2,2} of size 160
{4,10,2,2} of size 320
{5,10,2,2} of size 400
{3,10,2,2} of size 480
{3,10,2,2} of size 480
{5,10,2,2} of size 480
{5,10,2,2} of size 480
{6,10,2,2} of size 480
{8,10,2,2} of size 640
{4,10,2,2} of size 800
{10,10,2,2} of size 800
{10,10,2,2} of size 800
{10,10,2,2} of size 800
{12,10,2,2} of size 960
{4,10,2,2} of size 960
{4,10,2,2} of size 960
{6,10,2,2} of size 960
{6,10,2,2} of size 960
{3,10,2,2} of size 960
{5,10,2,2} of size 960
{6,10,2,2} of size 960
{6,10,2,2} of size 960
{6,10,2,2} of size 960
{6,10,2,2} of size 960
{10,10,2,2} of size 960
{10,10,2,2} of size 960
{10,10,2,2} of size 960
{10,10,2,2} of size 960
{14,10,2,2} of size 1120
{3,10,2,2} of size 1200
{6,10,2,2} of size 1200
{15,10,2,2} of size 1200
{16,10,2,2} of size 1280
{5,10,2,2} of size 1280
{4,10,2,2} of size 1280
{4,10,2,2} of size 1280
{5,10,2,2} of size 1280
{18,10,2,2} of size 1440
{3,10,2,2} of size 1440
{15,10,2,2} of size 1440
{20,10,2,2} of size 1600
{20,10,2,2} of size 1600
{20,10,2,2} of size 1600
{4,10,2,2} of size 1600
{22,10,2,2} of size 1760
{24,10,2,2} of size 1920
{4,10,2,2} of size 1920
{4,10,2,2} of size 1920
{12,10,2,2} of size 1920
{12,10,2,2} of size 1920
{12,10,2,2} of size 1920
{12,10,2,2} of size 1920
{20,10,2,2} of size 1920
{20,10,2,2} of size 1920
{4,10,2,2} of size 1920
{6,10,2,2} of size 1920
{6,10,2,2} of size 1920
{10,10,2,2} of size 1920
{6,10,2,2} of size 1920
{25,10,2,2} of size 2000
{5,10,2,2} of size 2000
{10,10,2,2} of size 2000
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,2,2}*40
5-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,2,2}*160, {10,2,4}*160, {10,4,2}*160
3-fold covers : {10,2,6}*240, {10,6,2}*240, {30,2,2}*240
4-fold covers : {20,4,2}*320, {20,2,4}*320, {10,4,4}*320, {40,2,2}*320, {10,2,8}*320, {10,8,2}*320
5-fold covers : {50,2,2}*400, {10,2,10}*400, {10,10,2}*400a, {10,10,2}*400c
6-fold covers : {10,2,12}*480, {10,12,2}*480, {20,2,6}*480, {20,6,2}*480a, {10,4,6}*480, {10,6,4}*480a, {60,2,2}*480, {30,2,4}*480, {30,4,2}*480a
7-fold covers : {10,2,14}*560, {10,14,2}*560, {70,2,2}*560
8-fold covers : {20,4,4}*640, {40,4,2}*640a, {20,4,2}*640, {40,4,2}*640b, {20,8,2}*640a, {20,8,2}*640b, {40,2,4}*640, {20,2,8}*640, {10,4,8}*640a, {10,8,4}*640a, {10,4,8}*640b, {10,8,4}*640b, {10,4,4}*640, {80,2,2}*640, {10,2,16}*640, {10,16,2}*640
9-fold covers : {10,2,18}*720, {10,18,2}*720, {90,2,2}*720, {10,6,6}*720a, {10,6,6}*720b, {10,6,6}*720c, {30,6,2}*720a, {30,2,6}*720, {30,6,2}*720b, {30,6,2}*720c
10-fold covers : {100,2,2}*800, {50,2,4}*800, {50,4,2}*800, {10,2,20}*800, {10,20,2}*800a, {20,2,10}*800, {20,10,2}*800a, {20,10,2}*800b, {10,4,10}*800, {10,10,4}*800a, {10,10,4}*800c, {10,20,2}*800c
11-fold covers : {10,2,22}*880, {10,22,2}*880, {110,2,2}*880
12-fold covers : {20,2,12}*960, {10,4,12}*960, {10,12,4}*960a, {20,4,6}*960, {20,6,4}*960a, {10,2,24}*960, {10,24,2}*960, {40,2,6}*960, {40,6,2}*960, {10,6,8}*960, {10,8,6}*960, {20,12,2}*960, {60,4,2}*960a, {60,2,4}*960, {30,4,4}*960, {120,2,2}*960, {30,2,8}*960, {30,8,2}*960, {10,4,6}*960, {10,6,4}*960e, {10,6,6}*960, {20,6,2}*960c, {30,6,2}*960, {30,4,2}*960
13-fold covers : {10,2,26}*1040, {10,26,2}*1040, {130,2,2}*1040
14-fold covers : {20,2,14}*1120, {20,14,2}*1120, {10,2,28}*1120, {10,28,2}*1120, {10,4,14}*1120, {10,14,4}*1120, {140,2,2}*1120, {70,2,4}*1120, {70,4,2}*1120
15-fold covers : {50,2,6}*1200, {50,6,2}*1200, {150,2,2}*1200, {10,6,10}*1200, {10,10,6}*1200a, {10,10,6}*1200c, {10,30,2}*1200a, {10,2,30}*1200, {10,30,2}*1200b, {30,2,10}*1200, {30,10,2}*1200b, {30,10,2}*1200c
16-fold covers : {10,4,8}*1280a, {10,8,4}*1280a, {20,8,2}*1280a, {40,4,2}*1280a, {10,8,8}*1280a, {10,8,8}*1280b, {10,8,8}*1280c, {40,8,2}*1280a, {40,8,2}*1280b, {40,8,2}*1280c, {10,8,8}*1280d, {40,8,2}*1280d, {40,2,8}*1280, {20,4,8}*1280a, {40,4,4}*1280a, {20,4,8}*1280b, {40,4,4}*1280b, {20,8,4}*1280a, {20,4,4}*1280a, {20,4,4}*1280b, {20,8,4}*1280b, {20,8,4}*1280c, {20,8,4}*1280d, {10,4,16}*1280a, {10,16,4}*1280a, {20,16,2}*1280a, {80,4,2}*1280a, {10,4,16}*1280b, {10,16,4}*1280b, {20,16,2}*1280b, {80,4,2}*1280b, {10,4,4}*1280, {10,4,8}*1280b, {10,8,4}*1280b, {20,4,2}*1280a, {40,4,2}*1280b, {20,8,2}*1280b, {20,2,16}*1280, {80,2,4}*1280, {10,2,32}*1280, {10,32,2}*1280, {160,2,2}*1280, {10,4,2}*1280b
17-fold covers : {10,2,34}*1360, {10,34,2}*1360, {170,2,2}*1360
18-fold covers : {10,2,36}*1440, {10,36,2}*1440, {20,2,18}*1440, {20,18,2}*1440a, {10,4,18}*1440, {10,18,4}*1440a, {180,2,2}*1440, {90,2,4}*1440, {90,4,2}*1440a, {10,6,12}*1440a, {10,6,12}*1440b, {10,12,6}*1440a, {10,12,6}*1440b, {20,6,6}*1440a, {20,6,6}*1440b, {20,6,6}*1440c, {60,6,2}*1440a, {30,12,2}*1440a, {10,6,12}*1440c, {10,12,6}*1440c, {30,6,4}*1440a, {30,2,12}*1440, {30,12,2}*1440b, {60,2,6}*1440, {60,6,2}*1440b, {60,6,2}*1440c, {30,4,6}*1440, {30,6,4}*1440b, {30,6,4}*1440c, {30,12,2}*1440c, {10,4,4}*1440, {10,4,6}*1440c, {10,6,4}*1440, {20,4,2}*1440, {30,4,2}*1440, {20,6,2}*1440
19-fold covers : {10,2,38}*1520, {10,38,2}*1520, {190,2,2}*1520
20-fold covers : {100,4,2}*1600, {100,2,4}*1600, {50,4,4}*1600, {200,2,2}*1600, {50,2,8}*1600, {50,8,2}*1600, {20,2,20}*1600, {20,10,4}*1600a, {10,4,20}*1600, {10,20,4}*1600a, {20,4,10}*1600, {10,2,40}*1600, {10,40,2}*1600a, {40,2,10}*1600, {40,10,2}*1600a, {40,10,2}*1600b, {10,8,10}*1600, {10,10,8}*1600a, {20,20,2}*1600a, {20,20,2}*1600c, {20,10,4}*1600b, {10,10,8}*1600c, {10,40,2}*1600c, {10,20,4}*1600c
21-fold covers : {10,6,14}*1680, {10,14,6}*1680, {30,2,14}*1680, {30,14,2}*1680, {10,2,42}*1680, {10,42,2}*1680, {70,2,6}*1680, {70,6,2}*1680, {210,2,2}*1680
22-fold covers : {20,2,22}*1760, {20,22,2}*1760, {10,2,44}*1760, {10,44,2}*1760, {10,4,22}*1760, {10,22,4}*1760, {220,2,2}*1760, {110,2,4}*1760, {110,4,2}*1760
23-fold covers : {10,2,46}*1840, {10,46,2}*1840, {230,2,2}*1840
24-fold covers : {60,4,4}*1920, {20,12,4}*1920a, {20,4,12}*1920, {30,4,8}*1920a, {30,8,4}*1920a, {60,8,2}*1920a, {120,4,2}*1920a, {10,8,12}*1920a, {10,12,8}*1920a, {20,8,6}*1920a, {10,4,24}*1920a, {10,24,4}*1920a, {40,4,6}*1920a, {40,12,2}*1920a, {20,24,2}*1920a, {30,4,8}*1920b, {30,8,4}*1920b, {60,8,2}*1920b, {120,4,2}*1920b, {10,8,12}*1920b, {10,12,8}*1920b, {20,8,6}*1920b, {10,4,24}*1920b, {10,24,4}*1920b, {40,4,6}*1920b, {40,12,2}*1920b, {20,24,2}*1920b, {30,4,4}*1920a, {60,4,2}*1920a, {10,4,12}*1920a, {10,12,4}*1920a, {20,4,6}*1920a, {20,12,2}*1920a, {60,2,8}*1920, {120,2,4}*1920, {20,6,8}*1920, {40,6,4}*1920a, {40,2,12}*1920, {20,2,24}*1920, {30,2,16}*1920, {30,16,2}*1920, {240,2,2}*1920, {10,6,16}*1920, {10,16,6}*1920, {10,2,48}*1920, {10,48,2}*1920, {80,2,6}*1920, {80,6,2}*1920, {10,4,12}*1920b, {10,12,4}*1920b, {20,12,2}*1920b, {20,4,6}*1920b, {20,6,4}*1920a, {20,6,6}*1920, {20,6,2}*1920a, {60,6,2}*1920a, {10,4,6}*1920, {10,4,12}*1920c, {10,6,4}*1920b, {10,6,12}*1920a, {10,12,4}*1920c, {10,12,6}*1920a, {20,6,4}*1920b, {30,12,2}*1920a, {30,6,2}*1920, {40,6,2}*1920b, {10,6,8}*1920a, {10,6,12}*1920b, {10,8,6}*1920a, {10,12,6}*1920b, {40,6,2}*1920c, {60,6,2}*1920b, {10,6,6}*1920, {10,6,8}*1920b, {10,8,6}*1920b, {30,6,4}*1920, {20,12,2}*1920c, {30,12,2}*1920b, {60,4,2}*1920b, {30,4,4}*1920d, {30,4,2}*1920b, {60,4,2}*1920c, {30,8,2}*1920b, {30,8,2}*1920c
25-fold covers : {250,2,2}*2000, {10,2,50}*2000, {10,50,2}*2000a, {50,2,10}*2000, {50,10,2}*2000a, {50,10,2}*2000b, {10,10,10}*2000a, {10,10,2}*2000a, {10,10,2}*2000c, {10,10,10}*2000b, {10,10,10}*2000c, {10,10,10}*2000e, {10,10,10}*2000g, {10,10,2}*2000d
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (11,12);;
s3 := (13,14);;
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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, 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(14)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(14)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(14)!(11,12);
s3 := Sym(14)!(13,14);
poly := sub<Sym(14)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope