# The 12-hosohedron

### Statistics

 genus c 0, orientable Schläfli formula c {2,12} V / F / E c 2 / 12 / 12 notes vertex, face multiplicity c 12, 1 Petrie polygonsholes2nd-order Petrie polygons3rd-order holes3rd-order Petrie polygons4th-order holes4th-order Petrie polygons5th-order holes5th-order Petrie polygons6th-order holes 2, each with 12 edges12, each with 2 edges4, each with 6 edges12, each with 2 edges6, each with 4 edges12, each with 2 edges4, each with 6 edges12, each with 2 edges2, each with 12 edges12, each with 2 edges antipodal sets 1 of ( 2v ), 6 of ( 2f, 2h3, 2h5; 2p3 ), 6 of ( 2e, 2h2, 2h4, 2h6 ), 2 of ( 2p2, 2p4 ) rotational symmetry group D24, with 24 elements full symmetry group D24×C2, with 48 elements its presentation c < r, s, t | r2, s2, t2, (rs)2, (st)12, (rt)2 > C&D number c R0.n12 The statistics marked c are from the published work of Professor Marston Conder.

### Relations to other Regular Maps

Its dual is the di-dodecagon.

Its Petrie dual is S5:{12,12}.

It is a 2-fold cover of the hemi-12-hosohedron.

It can be rectified to give the 12-lucanicohedron.

It is its own 5-hole derivative.

### Underlying Graph

Its skeleton is 12 . K2.

 D24

 C12×C2