Polytope of Type {2,28}

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

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)(23,24)
(25,28)(26,27)(29,30);;
s2 := ( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,23)(14,25)(16,19)(18,21)
(20,29)(22,26)(24,27)(28,30);;
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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(30)!(1,2);
s1 := Sym(30)!( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)
(23,24)(25,28)(26,27)(29,30);
s2 := Sym(30)!( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,23)(14,25)(16,19)
(18,21)(20,29)(22,26)(24,27)(28,30);
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope