#unrolling

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,…

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…

Buckminster Fuller used the term “dymaxion” for a variety of his designs, and one of these was the dymaxion map. It was based on the geometry of a polyhedron. While the dymaxion map is more directly related to the icosahedron, Fuller’s work often involved using other polyhedral shapes. One of them is the cuboctahedron. He used this term for various conceptual and practical designs, particularly in the context of his ideas on efficiency and structure. The cuboctahedron itself is notable…

A Buckyball, (or Fullerene), is a molecule of 60 carbon atoms with a structure resembling a soccer ball. It is a specific type of fullerene, often referred to as C60, where the carbon atoms form a series of pentagons and hexagons in a pattern that creates a spherical shape. This structure is similar to the arrangement found in a truncated icosahedron, with 12 pentagonal and 20 hexagonal faces. The buckyball is named after architect Buckminster Fuller, who popularized geodesic domes,…

Truncation in mathematics and geometry refers to cutting off parts of a shape, typically the vertices, edges, or other extremities, to create a new modified figure. This process is often used with polygons, polyhedra, or functions. A truncated tetrahedron is a polyhedron we can derive from a regular tetrahedron by truncating (cutting off) its four vertices. This process creates a new shape with additional faces while maintaining its symmetry. In this tutorial video, I am modeling and unrolling a truncated…

A cube is a three-dimensional shape with six square faces, twelve edges, and eight vertices. It is one of the most familiar geometric solids and is a special type of rectangular prism where all sides are of equal length. A cube has a high degree of symmetry. Angles between its faces are right angles. It is often referred to as a “regular hexahedron”. Also cube is one of the Platonic solids, known for its perfect symmetry and simplicity. Nevertheless, the…

A dodecahedron is a three-dimensional polyhedron with twelve flat, regular pentagonal faces, twenty vertices, and thirty edges. It is one of the Platonic solids and is highly symmetrical, with each face being a regular pentagon. The dodecahedron’s shape is unique among the Platonic solids because its faces are polygons with five sides, unlike the others which have triangular faces. Due to its symmetry, the dodecahedron has been used in various applications, including as a model in geometry and in certain…

An icosahedron is a three-dimensional polyhedron with twenty triangular faces, twelve vertices, and thirty edges. It is one of the five Platonic solids and is highly symmetrical, with all faces being equilateral triangles. A regular icosahedron has equal edge lengths and angles between its faces, making it one of the most symmetrical shapes in three-dimensional space. In this short tutorial video, I am modeling and unrolling an icosahedron. I studied this beautiful solid here, here, and here before. The Icosahedron…

An octahedron is a three-dimensional polyhedron with eight triangular faces, six vertices, and twelve edges. It is one of the Platonic solids and has high symmetry, with all of its faces being equilateral triangles. A regular octahedron can be visualized as two pyramids joined at their bases. It has the same number of faces as a cube has vertices, and the same number of vertices as a cube has faces. The octahedron is also dual to the cube, meaning that…

A tetrahedron is a three-dimensional shape with four triangular faces, four vertices, and six edges. It is the simplest polyhedron and, in its regular form, has equilateral triangles as faces, with all edges of equal length. Thus, known as one of the Platonic solids, a regular tetrahedron is highly symmetrical, and its shape is considered stable and efficient in many natural and man-made structures. In this short tutorial video, I am modeling and unrolling a tetrahedron. I studied this platonic…