# Polyhedron Category C1: Compound Regulars

The regular compounds have congruent faces, congruent edges, and congruent vertices. Also all of their faces are also regular. The first three are truly regular, the next two are very close to being regular. The last one isn't regular, but it belongs in the se regiment. All of these are orientable, except for hirki.

C1. So - (SO) stella octangula, or stellated octahedron. Faces are 8 triangles. It is a compound of 2 tets. It has 8 vertices and its verf is a triangle.

C2. Ki - (KI) chiricosahedron. Faces are 20 triangles. It is a compound of 5 tets and it is chiral. It has 20 vertices and its verf is a triangle.

C3. E - (E) icosicosahedron. Faces are 40 triangles, which are paired up. It is a compound of 10 tets. It has 40 vertices which are paired up into 20 fissary ones. Its verf is a 2-triangle compound.

C4. Rhom - (ROM) rhombihedron. Faces are 30 squares, it is in the sidtid regiment. It is the compound of 5 cubes. It has 40 vertices which are paired up into 20 fissary ones. Its verf is a 2-triangle compound. Rhom shows up as a combocell in several uniform polychora.

C5. Se - (SEE) small icosicosahedron. Faces are 40 triangles, which are paired up. It is a compound of 5 octs. It has 30 vertices and its verf is a square.

C6. Hirki - (HUR kee) hemirhombichiricosahedron. Faces are 20 triangles and 15 central squares. It is a compound of 5 thahs, it is chiral. It has 30 vertices and its verf is a bowtie, it is in the se regiment.

Dual Pairs: rhom-se.

Self Dual: so, ki, e.

Self Conjugates: so, ki, e, rhom, se, hirki.