In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex. The term originates from Kepler 's names for the Archimedean solids.

While a frustum and a truncated solid may seem similar at first glance, they are two distinct shapes with unique properties. A frustum is derived by slicing a solid with two parallel planes, whereas a truncated solid is derived by slicing a solid with a plane that is not parallel to its base.

In geometry, the truncated icosahedron is a polyhedron that can be constructed by truncating all of the regular icosahedron's vertices. Intuitively, it may be regarded as footballs (or soccer balls) that are typically patterned with white hexagons and black pentagons.

Seven of the 13 Archimedean solids (the cuboctahedron, icosidodecahedron, truncated cube, truncated dodecahedron, truncated octahedron, truncated icosahedron, and truncated tetrahedron) can be obtained by truncation of a Platonic solid. The three truncation series producing these seven Archimedean solids are illustrated above.

Truncating P P at a vertex v v consists of marking the midpoints of the edges that touch v v and then slicing off a corner of P P by the plane that passes through all those points. For each Platonic solid P P, determine the the polyhedron that results from truncating P …

What's the difference between frustum and truncated? (n.) The part of a solid next the base, formed by cutting off the, top; or the part of any solid, as of a cone, pyramid, etc., between two planes, which may be either parallel or inclined to each other. (n.) One of the drums of the shaft of a …

Each truncated solid defines 4 concentric spheres due to the larger faces having the smaller inspheres touching their centers. Each can sit neatly inside their original Platonic Solid & its Dual. We saw the first two Archimedean solids above.

A truncated solid is a solid that has been cut by a plane and has only a portion of the separated sections remaining. In this case, the expression "a picture is worth a thousand words" takes on its full meaning. Instead of listing the different construction characteristics of these solids, here are some examples.

The document discusses different types of truncated and frustum solids. It provides examples of drawing orthographic views of these solids in different orientations and when cut by planes parallel or inclined to the base.

Truncated When a solid(prism/cylinder/pyramid/cone) is cut by a cutting plane inclined to its base (not parallel) the remaining portion thus obtained after removing the top portion is called the truncated solid. In first stage, it is assumed to be kept such that …