Studios

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…

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, 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…

A truncated cuboctahedron is an Archimedean solid, meaning it is a highly symmetrical, convex polyhedron with identical vertices and faces of regular polygons. As its name suggests, you can create the truncated cuboctahedron by truncating (cutting off) the vertices of a cuboctahedron. A cuboctahedron is a rectified cube. After you model it, you can divide all its edges into 1/3s. Then, connect those division points to draw the squares, hexagons, and octagons. In this short tutorial video, I am folding…

An icosidodecahedron is a polyhedron that is part of the family of Archimedean solids. It has 32 faces, consisting of 12 regular pentagonal faces of a dodecahedron and 20 regular triangular faces of an icosahedron. It is highly symmetrical, with the same arrangement of faces around each vertex. In this short tutorial video, I am modeling and unrolling an icosidodecahedron. This polyhedron is very interesting and is mostly used as a basis for more sophisticated designs. Its dual polyhedron is a rhombic triacontahedron,…

Stellation of polyhedra refers to the process of extending the faces (or edges) of a polyhedron outward to form new, more complex shapes. These new shapes, called stellations, are created by adding extra vertices, edges, and faces that “project” outward from the original polyhedron’s structure. You can create an infinite number of new polyhedral forms, depending on how you extend the faces and edges. In this short tutorial video, I am modeling a stellated icosahedron. I use basic modeling commands…

A dual polyhedron is a concept in geometry where two polyhedra are related in such a way that the vertices of one polyhedron correspond to the faces of the other, and the faces of the first polyhedron correspond to the vertices of the second. The process of creating a dual polyhedron is called duality, and it applies to many regular, semi-regular, and some irregular polyhedra. In the case of Platonic solids, the cube and octahedron are duals of each other….

The truncated octahedron is an Archimedean solid, characterized by a mix of hexagonal and square faces, and it has a very symmetrical and regular structure. Buckminster Fuller called this solid “Mecon”. The truncation process includes the cutting the edges of a polyhedron. We do this by dividing every edge of the polyhedron into 1/3s. Then, we carefully re-connect these division points to generate new, planar polygons. In the case of a truncated octahedron, we transform the 8 regular triangular faces…