#polyhedron

I also wanted to draw Peter Stamatin

And revive my Tumblr acc a bit :P

The octahedron has exactly 4x the volume of the tetrahedron.

The cuboctahedron is 20x the tetrahedron

the truncated tetrahedron is 23x the tetrahedron

the truncated octahedron is 96x the tetrahedron

The great icosidodecahedron is a uniform star polyhedron. It has 32 faces (20 triangles, 12 pentagrams), 60 edges, and 30 vertices. It can be constructed through rectification of the great stellated dodecahedron or the great icosahedron. It shares its vertex arrangement with the icosidodecahedron, and its edge arrangement with the great icosihemidodecahedron and the great dodecahemidodecahedron. Its dual is the great rhombic triacontahedron.

This is a polyhedron with cutaway faces, based on the snub dodecadodecahedron, which I posted here some time ago. In this version there is a single connected piece for each face, instead of multiple disconnected facets. I designed the model faces so that they avoid each other when assembled, with the holes making the interior of the model visible.

This isohedral heptagrammic hexecontahedron is a non-convex polyhedron with 60 faces, 210 edges, and 104 vertices. It is the dual of a near-miss uniform snub icosidisdodecahedron.

The tortuous tunnel (or M, in Stewart notation) is a quasi-convex Stewart toroid. It has 24 faces (6 squares, 18 triangles), 39 edges, and 15 vertices. It has the fewest vertices of any known quasi-convex Stewart toroid. It can be constructed by excavating two octahedra from a triangular orthobicupola.

The elongated triangular cupola is a Johnson solid (J18). It has 14 faces (4 triangles, 9 squares, 1 hexagon), 27 edges, and 15 vertices. It is constructed by attaching a hexagonal prism to the base of the triangular cupola. Its dual is not uniquely named.

The joined truncated octahedron is a convex polyhedron with 36 faces, 72 edges, and 38 vertices. Its dual is the rectified truncated octahedron.