# The 14-hosohedron

### Statistics

 genus c 0, orientable Schläfli formula c {2,14} V / F / E c 2 / 14 / 14 notes vertex, face multiplicity c 14, 1 Petrie polygonsholes2nd-order Petrie polygons3rd-order holes3rd-order Petrie polygons4th-order holes4th-order Petrie polygons5th-order holes5th-order Petrie polygons6th-order holes6th-order Petrie polygons7th-order holes 2, each with 14 edges14, each with 2 edges2, each with 14 edges14, each with 2 edges2, each with 14 edges14, each with 2 edges2, each with 14 edges14, each with 2 edges2, each with 14 edges14, each with 2 edges2, each with 14 edges14, each with 2 edges antipodal sets 1 of ( 2v ), 7 of ( 2f, 2h3, 2h5, 2h7 ), 7 of ( 2e, 2h2, 2h4, 2h6 ), 1 of ( 2p1, 2pp3, 2p5 ), of ( 1 of ( 2p2, 2p4, 2p6 ) rotational symmetry group D28, with 28 elements full symmetry group D28×C2, with 56 elements its presentation c < r, s, t | r2, s2, t2, (rs)2, (st)14, (rt)2 > C&D number c R0.n14 The statistics marked c are from the published work of Professor Marston Conder.

### Relations to other Regular Maps

Its dual is the di-14gon.

Its Petrie dual is S6:{14,14}.

It is a 2-fold cover of the hemi-14-hosohedron.

It can be rectified to give the 14-lucanicohedron.

It is its own 3-hole derivative.
It is its own 5-hole derivative.

### Underlying Graph

Its skeleton is 14 . K2.

### Cayley Graphs based in this Regular Map

 D28

#### Type IIa

 C7×C2×C2