Polyhedron Category C3: Fivers


Here are three regiments of three, each regiment contains two orientables and a non-orientable. Each of these is a compound of 5 polyhedra, where the polyhedron has cubic symmetry, the whole compound has doic symmetry. Iddei, gari, and rasquahr look quite different due to neo-filling.

C12. Arie - (AIR ee) antirhombicosicosahedron. Faces are 40 triangles (20 pairs) and 30 squares. It is a compound of 5 coes. It has 60 vertices and its verf is a rectangle.

C13. Iddei - (id DI) icosidisicosahedron. Faces are 40 triangles (20 pairs) and 20 hexagons (10 central pairs). It is a compound of 5 ohoes. It has 60 vertices and its verf is a bowtie.

C14. Gari - (GAIR ee) great antirhombicosahedron. Faces are 20 hexagons (10 central pairs) and 30 squares. It is a compound of 5 choes. It has 60 vertices and its verf is a bowtie.

C15. Rasseri - (RAS sir ee) rhombisnub rhombicosicosahedron. Faces are 40 triangles (20 pairs), 30 squares, and 60 snub squares. It is a compound of 5 sircoes. It has 120 vertices and its verf is a trapezoid.

C16. Rahrie - (RAHR ee) rhombihyperhombicosicosahedron. Faces are 40 triangles (20 pairs), 30 squares, and 30 octagons. It is a compound of 5 soccoes. It has 120 vertices. Its verf is a crossed trapezoid.

C17. Rasher - (RASH er) rhombisnub hyperhombihedron. Faces are 60 snub squares and 30 octagons. It is a compound of 5 srohs. It has 120 vertices and its verf is a butterfly.

C18. Raquahri - (ra QUAH ree) rhombiquasihyperhombicosicosahedron. Faces are 40 triangles (20 pairs), 30 squares, and 30 octagrams. It is the compound of 5 goccoes. It has 120 vertices. Its verf is a trapezoid.

C19. Rosaqri - (ro ZAK ree) rhombisnub quasirhombicosicosahedron, previously called rhombisnub quasihyperpseudorhombicosicosahedron (rasquahpri). Faces are 40 triangles (20 pairs), 30 squares, and 60 snub squares. It is a compound of 5 quercoes. It has 120 vertices and its verf is crossed trapezoid.

C20. Rasquahr - (ras QUAHR) rhombisnub quasihyperhombihedron. Faces are 60 snub squares and 30 octagrams. It is the compound of 5 grohs. It has 120 vertices. Its verf is a butterfly.


Below are the traditional fillings for iddei, gari, and rasquahr.


Conjugate Pairs: rasseri-rosaqri, rahrie-raquahri, rasher-rasquahr.

Self Conjugates: arie, iddei, gari.


Category C2: Compound Truncates . . . Polyhedron Page . . . Category C4: Ikers