Polytope of Type {28}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28}*56
Also Known As : 28-gon, {28}. if this polytope has another name.
Group : SmallGroup(56,5)
Rank : 2
Schlafli Type : {28}
Number of vertices, edges, etc : 28, 28
Order of s0s1 : 28
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{28,2} of size 112
{28,4} of size 224
{28,6} of size 336
{28,6} of size 336
{28,4} of size 448
{28,8} of size 448
{28,8} of size 448
{28,6} of size 504
{28,10} of size 560
{28,12} of size 672
{28,6} of size 672
{28,14} of size 784
{28,14} of size 784
{28,14} of size 784
{28,8} of size 896
{28,4} of size 896
{28,8} of size 896
{28,16} of size 896
{28,16} of size 896
{28,18} of size 1008
{28,18} of size 1008
{28,4} of size 1008
{28,6} of size 1008
{28,20} of size 1120
{28,22} of size 1232
{28,12} of size 1344
{28,24} of size 1344
{28,24} of size 1344
{28,4} of size 1344
{28,4} of size 1344
{28,6} of size 1344
{28,6} of size 1344
{28,8} of size 1344
{28,8} of size 1344
{28,8} of size 1344
{28,8} of size 1344
{28,3} of size 1344
{28,6} of size 1344
{28,6} of size 1344
{28,7} of size 1344
{28,12} of size 1344
{28,6} of size 1344
{28,12} of size 1344
{28,10} of size 1400
{28,26} of size 1456
{28,6} of size 1512
{28,28} of size 1568
{28,28} of size 1568
{28,28} of size 1568
{28,4} of size 1568
{28,30} of size 1680
{28,6} of size 1680
{28,10} of size 1680
{28,30} of size 1680
{28,8} of size 1792
{28,16} of size 1792
{28,16} of size 1792
{28,32} of size 1792
{28,32} of size 1792
{28,4} of size 1792
{28,8} of size 1792
{28,8} of size 1792
{28,8} of size 1792
{28,34} of size 1904
Vertex Figure Of :
{2,28} of size 112
{4,28} of size 224
{6,28} of size 336
{6,28} of size 336
{4,28} of size 448
{8,28} of size 448
{8,28} of size 448
{6,28} of size 504
{10,28} of size 560
{12,28} of size 672
{6,28} of size 672
{14,28} of size 784
{14,28} of size 784
{14,28} of size 784
{8,28} of size 896
{4,28} of size 896
{8,28} of size 896
{16,28} of size 896
{16,28} of size 896
{18,28} of size 1008
{18,28} of size 1008
{4,28} of size 1008
{6,28} of size 1008
{20,28} of size 1120
{22,28} of size 1232
{12,28} of size 1344
{24,28} of size 1344
{24,28} of size 1344
{4,28} of size 1344
{4,28} of size 1344
{6,28} of size 1344
{6,28} of size 1344
{8,28} of size 1344
{8,28} of size 1344
{8,28} of size 1344
{8,28} of size 1344
{3,28} of size 1344
{6,28} of size 1344
{6,28} of size 1344
{7,28} of size 1344
{12,28} of size 1344
{6,28} of size 1344
{12,28} of size 1344
{10,28} of size 1400
{26,28} of size 1456
{6,28} of size 1512
{28,28} of size 1568
{28,28} of size 1568
{28,28} of size 1568
{4,28} of size 1568
{30,28} of size 1680
{6,28} of size 1680
{10,28} of size 1680
{30,28} of size 1680
{8,28} of size 1792
{16,28} of size 1792
{16,28} of size 1792
{32,28} of size 1792
{32,28} of size 1792
{4,28} of size 1792
{8,28} of size 1792
{8,28} of size 1792
{8,28} of size 1792
{34,28} of size 1904
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {14}*28
4-fold quotients : {7}*14
7-fold quotients : {4}*8
14-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {56}*112
3-fold covers : {84}*168
4-fold covers : {112}*224
5-fold covers : {140}*280
6-fold covers : {168}*336
7-fold covers : {196}*392
8-fold covers : {224}*448
9-fold covers : {252}*504
10-fold covers : {280}*560
11-fold covers : {308}*616
12-fold covers : {336}*672
13-fold covers : {364}*728
14-fold covers : {392}*784
15-fold covers : {420}*840
16-fold covers : {448}*896
17-fold covers : {476}*952
18-fold covers : {504}*1008
19-fold covers : {532}*1064
20-fold covers : {560}*1120
21-fold covers : {588}*1176
22-fold covers : {616}*1232
23-fold covers : {644}*1288
24-fold covers : {672}*1344
25-fold covers : {700}*1400
26-fold covers : {728}*1456
27-fold covers : {756}*1512
28-fold covers : {784}*1568
29-fold covers : {812}*1624
30-fold covers : {840}*1680
31-fold covers : {868}*1736
32-fold covers : {896}*1792
33-fold covers : {924}*1848
34-fold covers : {952}*1904
35-fold covers : {980}*1960
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20)(21,22)
(23,26)(24,25)(27,28);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,21)(12,23)(14,17)(16,19)
(18,27)(20,24)(22,25)(26,28);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(28)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20)
(21,22)(23,26)(24,25)(27,28);
s1 := Sym(28)!( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,21)(12,23)(14,17)
(16,19)(18,27)(20,24)(22,25)(26,28);
poly := sub<Sym(28)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope