Polytope of Type {2,14,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,2}*112
if this polytope has a name.
Group : SmallGroup(112,42)
Rank : 4
Schlafli Type : {2,14,2}
Number of vertices, edges, etc : 2, 14, 14, 2
Order of s₀s₁s₂s₃ : 14
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,14,2,2} of size 224
   {2,14,2,3} of size 336
   {2,14,2,4} of size 448
   {2,14,2,5} of size 560
   {2,14,2,6} of size 672
   {2,14,2,7} of size 784
   {2,14,2,8} of size 896
   {2,14,2,9} of size 1008
   {2,14,2,10} of size 1120
   {2,14,2,11} of size 1232
   {2,14,2,12} of size 1344
   {2,14,2,13} of size 1456
   {2,14,2,14} of size 1568
   {2,14,2,15} of size 1680
   {2,14,2,16} of size 1792
   {2,14,2,17} of size 1904
Vertex Figure Of :
   {2,2,14,2} of size 224
   {3,2,14,2} of size 336
   {4,2,14,2} of size 448
   {5,2,14,2} of size 560
   {6,2,14,2} of size 672
   {7,2,14,2} of size 784
   {8,2,14,2} of size 896
   {9,2,14,2} of size 1008
   {10,2,14,2} of size 1120
   {11,2,14,2} of size 1232
   {12,2,14,2} of size 1344
   {13,2,14,2} of size 1456
   {14,2,14,2} of size 1568
   {15,2,14,2} of size 1680
   {16,2,14,2} of size 1792
   {17,2,14,2} of size 1904
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,7,2}*56
   7-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,28,2}*224, {2,14,4}*224, {4,14,2}*224
   3-fold covers : {2,14,6}*336, {6,14,2}*336, {2,42,2}*336
   4-fold covers : {2,28,4}*448, {4,28,2}*448, {4,14,4}*448, {2,56,2}*448, {2,14,8}*448, {8,14,2}*448
   5-fold covers : {2,14,10}*560, {10,14,2}*560, {2,70,2}*560
   6-fold covers : {2,14,12}*672, {12,14,2}*672, {2,28,6}*672a, {6,28,2}*672a, {4,14,6}*672, {6,14,4}*672, {2,84,2}*672, {2,42,4}*672a, {4,42,2}*672a
   7-fold covers : {2,98,2}*784, {2,14,14}*784a, {2,14,14}*784c, {14,14,2}*784a, {14,14,2}*784b
   8-fold covers : {4,28,4}*896, {2,56,4}*896a, {4,56,2}*896a, {2,28,4}*896, {4,28,2}*896, {2,56,4}*896b, {4,56,2}*896b, {2,28,8}*896a, {8,28,2}*896a, {2,28,8}*896b, {8,28,2}*896b, {4,14,8}*896, {8,14,4}*896, {2,112,2}*896, {2,14,16}*896, {16,14,2}*896
   9-fold covers : {2,14,18}*1008, {18,14,2}*1008, {2,126,2}*1008, {6,14,6}*1008, {2,42,6}*1008a, {6,42,2}*1008a, {2,42,6}*1008b, {2,42,6}*1008c, {6,42,2}*1008b, {6,42,2}*1008c
   10-fold covers : {2,14,20}*1120, {20,14,2}*1120, {2,28,10}*1120, {10,28,2}*1120, {4,14,10}*1120, {10,14,4}*1120, {2,140,2}*1120, {2,70,4}*1120, {4,70,2}*1120
   11-fold covers : {2,14,22}*1232, {22,14,2}*1232, {2,154,2}*1232
   12-fold covers : {4,14,12}*1344, {12,14,4}*1344, {4,28,6}*1344, {6,28,4}*1344, {2,14,24}*1344, {24,14,2}*1344, {2,56,6}*1344, {6,56,2}*1344, {6,14,8}*1344, {8,14,6}*1344, {2,28,12}*1344, {12,28,2}*1344, {2,84,4}*1344a, {4,84,2}*1344a, {4,42,4}*1344a, {2,168,2}*1344, {2,42,8}*1344, {8,42,2}*1344, {2,28,6}*1344, {2,42,6}*1344, {6,28,2}*1344, {6,42,2}*1344, {2,42,4}*1344, {4,42,2}*1344
   13-fold covers : {2,14,26}*1456, {26,14,2}*1456, {2,182,2}*1456
   14-fold covers : {2,196,2}*1568, {2,98,4}*1568, {4,98,2}*1568, {2,14,28}*1568a, {2,28,14}*1568a, {2,28,14}*1568b, {14,28,2}*1568a, {14,28,2}*1568b, {28,14,2}*1568a, {4,14,14}*1568a, {4,14,14}*1568b, {14,14,4}*1568a, {14,14,4}*1568b, {2,14,28}*1568c, {28,14,2}*1568c
   15-fold covers : {6,14,10}*1680, {10,14,6}*1680, {2,14,30}*1680, {30,14,2}*1680, {2,42,10}*1680, {10,42,2}*1680, {2,70,6}*1680, {6,70,2}*1680, {2,210,2}*1680
   16-fold covers : {2,28,8}*1792a, {8,28,2}*1792a, {2,56,4}*1792a, {4,56,2}*1792a, {2,56,8}*1792a, {8,56,2}*1792a, {2,56,8}*1792b, {2,56,8}*1792c, {8,56,2}*1792b, {8,56,2}*1792c, {2,56,8}*1792d, {8,56,2}*1792d, {8,14,8}*1792, {4,28,8}*1792a, {8,28,4}*1792a, {4,28,8}*1792b, {8,28,4}*1792b, {4,56,4}*1792a, {4,28,4}*1792a, {4,28,4}*1792b, {4,56,4}*1792b, {4,56,4}*1792c, {4,56,4}*1792d, {2,28,16}*1792a, {16,28,2}*1792a, {2,112,4}*1792a, {4,112,2}*1792a, {2,28,16}*1792b, {16,28,2}*1792b, {2,112,4}*1792b, {4,112,2}*1792b, {2,28,4}*1792, {2,56,4}*1792b, {4,28,2}*1792, {4,56,2}*1792b, {2,28,8}*1792b, {8,28,2}*1792b, {4,14,16}*1792, {16,14,4}*1792, {2,14,32}*1792, {32,14,2}*1792, {2,224,2}*1792
   17-fold covers : {2,14,34}*1904, {34,14,2}*1904, {2,238,2}*1904
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,16);;
s3 := (17,18);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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(18)!(1,2);
s1 := Sym(18)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s2 := Sym(18)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,16);
s3 := Sym(18)!(17,18);
poly := sub<Sym(18)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, 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