Polytope of Type {28,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,2}*112
if this polytope has a name.
Group : SmallGroup(112,29)
Rank : 3
Schlafli Type : {28,2}
Number of vertices, edges, etc : 28, 28, 2
Order of s0s1s2 : 28
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{28,2,2} of size 224
{28,2,3} of size 336
{28,2,4} of size 448
{28,2,5} of size 560
{28,2,6} of size 672
{28,2,7} of size 784
{28,2,8} of size 896
{28,2,9} of size 1008
{28,2,10} of size 1120
{28,2,11} of size 1232
{28,2,12} of size 1344
{28,2,13} of size 1456
{28,2,14} of size 1568
{28,2,15} of size 1680
{28,2,16} of size 1792
{28,2,17} of size 1904
Vertex Figure Of :
{2,28,2} of size 224
{4,28,2} of size 448
{6,28,2} of size 672
{6,28,2} of size 672
{4,28,2} of size 896
{8,28,2} of size 896
{8,28,2} of size 896
{6,28,2} of size 1008
{10,28,2} of size 1120
{12,28,2} of size 1344
{6,28,2} of size 1344
{14,28,2} of size 1568
{14,28,2} of size 1568
{14,28,2} of size 1568
{8,28,2} of size 1792
{16,28,2} of size 1792
{16,28,2} of size 1792
{4,28,2} of size 1792
{8,28,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {14,2}*56
4-fold quotients : {7,2}*28
7-fold quotients : {4,2}*16
14-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {28,4}*224, {56,2}*224
3-fold covers : {28,6}*336a, {84,2}*336
4-fold covers : {56,4}*448a, {28,4}*448, {56,4}*448b, {28,8}*448a, {28,8}*448b, {112,2}*448
5-fold covers : {28,10}*560, {140,2}*560
6-fold covers : {56,6}*672, {28,12}*672, {84,4}*672a, {168,2}*672
7-fold covers : {196,2}*784, {28,14}*784a, {28,14}*784b
8-fold covers : {56,4}*896a, {56,8}*896a, {56,8}*896b, {28,8}*896a, {56,8}*896c, {56,8}*896d, {112,4}*896a, {112,4}*896b, {28,4}*896, {56,4}*896b, {28,8}*896b, {28,16}*896a, {28,16}*896b, {224,2}*896
9-fold covers : {28,18}*1008a, {252,2}*1008, {84,6}*1008a, {84,6}*1008b, {84,6}*1008c, {28,6}*1008
10-fold covers : {56,10}*1120, {28,20}*1120, {140,4}*1120, {280,2}*1120
11-fold covers : {28,22}*1232, {308,2}*1232
12-fold covers : {112,6}*1344, {28,12}*1344a, {28,24}*1344a, {56,12}*1344a, {28,24}*1344b, {56,12}*1344b, {168,4}*1344a, {84,4}*1344a, {168,4}*1344b, {84,8}*1344a, {84,8}*1344b, {336,2}*1344, {28,6}*1344e, {84,6}*1344a, {84,4}*1344b
13-fold covers : {28,26}*1456, {364,2}*1456
14-fold covers : {196,4}*1568, {392,2}*1568, {56,14}*1568a, {56,14}*1568b, {28,28}*1568a, {28,28}*1568c
15-fold covers : {28,30}*1680a, {84,10}*1680, {140,6}*1680a, {420,2}*1680
16-fold covers : {56,8}*1792a, {28,8}*1792a, {56,8}*1792b, {56,4}*1792a, {56,8}*1792c, {56,8}*1792d, {28,16}*1792a, {112,4}*1792a, {28,16}*1792b, {112,4}*1792b, {112,8}*1792a, {56,16}*1792a, {112,8}*1792b, {56,16}*1792b, {56,16}*1792c, {112,8}*1792c, {112,8}*1792d, {56,16}*1792d, {56,16}*1792e, {112,8}*1792e, {112,8}*1792f, {56,16}*1792f, {28,32}*1792a, {224,4}*1792a, {28,32}*1792b, {224,4}*1792b, {28,4}*1792, {56,4}*1792b, {28,8}*1792b, {28,8}*1792c, {56,8}*1792e, {56,4}*1792c, {56,4}*1792d, {28,8}*1792d, {56,8}*1792f, {56,8}*1792g, {56,8}*1792h, {448,2}*1792
17-fold covers : {28,34}*1904, {476,2}*1904
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);;
s2 := (29,30);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2,
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(30)!( 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(30)!( 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);
s2 := Sym(30)!(29,30);
poly := sub<Sym(30)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2, 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 >;
to this polytope