# The 13-hosohedron

### Statistics

 genus c 0, orientable Schläfli formula c {2,13} V / F / E c 2 / 13 / 13 notes vertex, face multiplicity c 13, 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 polygons 1, with 26 edges13, each with 2 edges1, with 26 edges13, each with 2 edges1, with 26 edges13, each with 2 edges1, with 26 edges13, each with 2 edges1, with 26 edges13, each with 2 edges1, with 26 edges antipodal sets 1 of ( 2v ), 13 of ( f, e, h2, h3, h4, h5, h6 ) rotational symmetry group D26, with 26 elements full symmetry group D52, with 52 elements its presentation c < r, s, t | r2, s2, t2, (rs)2, (st)13, (rt)2 > C&D number c R0.n13 The statistics marked c are from the published work of Professor Marston Conder.

### Relations to other Regular Maps

Its dual is the di-13gon.

Its Petrie dual is S6:{26,13}.

It can be rectified to give the 13-lucanicohedron.

It is its own 2-hole derivative.
It is its own 3-hole derivative.
It is its own 4-hole derivative.
It is its own 5-hole derivative.
It is its own 6-hole derivative.

### Underlying Graph

Its skeleton is 13 . K2.

 D26

 C26