Polytope of Type {56}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56}*112
Also Known As : 56-gon, {56}. if this polytope has another name.
Group : SmallGroup(112,6)
Rank : 2
Schlafli Type : {56}
Number of vertices, edges, etc : 56, 56
Order of s0s1 : 56
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{56,2} of size 224
{56,4} of size 448
{56,4} of size 448
{56,6} of size 672
{56,4} of size 896
{56,8} of size 896
{56,8} of size 896
{56,8} of size 896
{56,8} of size 896
{56,4} of size 896
{56,10} of size 1120
{56,12} of size 1344
{56,12} of size 1344
{56,6} of size 1344
{56,6} of size 1344
{56,6} of size 1344
{56,14} of size 1568
{56,14} of size 1568
{56,14} of size 1568
{56,8} of size 1792
{56,8} of size 1792
{56,4} of size 1792
{56,8} of size 1792
{56,8} of size 1792
{56,16} of size 1792
{56,16} of size 1792
{56,16} of size 1792
{56,16} of size 1792
{56,16} of size 1792
{56,16} of size 1792
{56,4} of size 1792
{56,8} of size 1792
{56,4} of size 1792
{56,4} of size 1792
{56,8} of size 1792
{56,8} of size 1792
{56,8} of size 1792
Vertex Figure Of :
{2,56} of size 224
{4,56} of size 448
{4,56} of size 448
{6,56} of size 672
{4,56} of size 896
{8,56} of size 896
{8,56} of size 896
{8,56} of size 896
{8,56} of size 896
{4,56} of size 896
{10,56} of size 1120
{12,56} of size 1344
{12,56} of size 1344
{6,56} of size 1344
{6,56} of size 1344
{6,56} of size 1344
{14,56} of size 1568
{14,56} of size 1568
{14,56} of size 1568
{8,56} of size 1792
{8,56} of size 1792
{4,56} of size 1792
{8,56} of size 1792
{8,56} of size 1792
{16,56} of size 1792
{16,56} of size 1792
{16,56} of size 1792
{16,56} of size 1792
{16,56} of size 1792
{16,56} of size 1792
{4,56} of size 1792
{8,56} of size 1792
{4,56} of size 1792
{4,56} of size 1792
{8,56} of size 1792
{8,56} of size 1792
{8,56} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {28}*56
4-fold quotients : {14}*28
7-fold quotients : {8}*16
8-fold quotients : {7}*14
14-fold quotients : {4}*8
28-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {112}*224
3-fold covers : {168}*336
4-fold covers : {224}*448
5-fold covers : {280}*560
6-fold covers : {336}*672
7-fold covers : {392}*784
8-fold covers : {448}*896
9-fold covers : {504}*1008
10-fold covers : {560}*1120
11-fold covers : {616}*1232
12-fold covers : {672}*1344
13-fold covers : {728}*1456
14-fold covers : {784}*1568
15-fold covers : {840}*1680
16-fold covers : {896}*1792
17-fold covers : {952}*1904
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)(17,23)
(18,22)(24,25)(27,34)(28,33)(29,36)(30,35)(31,38)(32,37)(39,40)(41,46)(42,45)
(43,48)(44,47)(49,50)(51,54)(52,53)(55,56);;
s1 := ( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,27)(11,29)(13,31)(14,20)
(16,22)(18,24)(19,39)(21,41)(23,43)(25,32)(26,33)(28,35)(30,37)(34,49)(36,51)
(38,44)(40,45)(42,47)(46,55)(48,52)(50,53)(54,56);;
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*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(56)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)
(17,23)(18,22)(24,25)(27,34)(28,33)(29,36)(30,35)(31,38)(32,37)(39,40)(41,46)
(42,45)(43,48)(44,47)(49,50)(51,54)(52,53)(55,56);
s1 := Sym(56)!( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,27)(11,29)(13,31)
(14,20)(16,22)(18,24)(19,39)(21,41)(23,43)(25,32)(26,33)(28,35)(30,37)(34,49)
(36,51)(38,44)(40,45)(42,47)(46,55)(48,52)(50,53)(54,56);
poly := sub<Sym(56)|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*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