Drawing Herschels Enneahedron

The Herschel nonahedron is a canonical polyhedron whose skeleton is the Herschel graph. It has 11 vertices, 18 edges, and 9 faces. Of the edges, 6 are short and 12 are long. It is characterized by having nine faces (hence the prefix “ennea” meaning nine in Greek). In this short tutorial video, I am folding Herschel’s enneahedron. To do that, I am constructing the interior angles of this polyhedron using its unrolled net. First, I am drawing the net by…

In geometry, a truncated icosidodecahedron, rhombitruncated icosidodecahedron, great rhombicosidodecahedron, omnitruncated dodecahedron, or omnitruncated icosahedron is an Archimedean solid. It is one of thirteen convex, isogonal, non-prismatic solids constructed by two or more types of regular polygon faces. In this short tutorial, I am constructing an irregular truncated icosidodecahedron. It is not the regular Archimedean solid, but a rough approximation of it. I made this model to exercise the exploration of new polyhedra by using rectification and truncation operations. Nevertheless, here…

The sphenoid hendecahedron is a unique and interesting polyhedron. As the name implies, a “hendecahedron” is a polyhedron with 11 faces, while “sphenoid” refers to a specific type of shape that is often unusual, asymmetrical, and typically wedge-shaped. This polyhedron fills space, packing 3D space without gaps or overlaps. Its convex shape allows it to tessellate efficiently. Therefore, space-filling polyhedra play a crucial role in understanding tessellations and geometric arrangements, showing how to occupy 3D space without leaving any voids…

The rhombicosidodecahedron, an Archimedean solid, is one of the 13 convex polyhedra made up of regular polygons. While all its faces are congruent, they consist of various types of regular polygons. I previously explored this fascinating polyhedron and am revisiting it now as part of the Architectural Geometry course. In this short tutorial video, I demonstrate the modeling of a rhombicosidodecahedron. Despite its lengthy and unusual name, this polyhedron is truly a remarkable and beautiful structure. I hope that this…

In geometry, the excavated dodecahedron is a star polyhedron that looks like a dodecahedron with concave pentagonal pyramids in place of its faces. In this short tutorial video, I am modeling an excavated dodecahedron in the Rhinoceros software. I use basic drawing and modeling commands. I aim to introduce this skill to beginner-level architects and designers. As the name suggests, this process includes the construction of the dodecahedron first. Then, the pentagonal faces of this polyhedron were “excavated” to the…