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  2. Truncation (geometry) - Wikipedia

    en.wikipedia.org/wiki/Truncation_(geometry)

    Uniform truncation are a special case of this with equal edge lengths. The truncated cube, t{4,3}, with square faces becoming octagons, with new triangular faces are the vertices. Antitruncation A reverse shallow truncation, truncated outwards off the original edges, rather than inward. This results in a polytope which looks like the original ...

  3. Chamfer (geometry) - Wikipedia

    en.wikipedia.org/wiki/Chamfer_(geometry)

    In geometry, chamfering or edge-truncation is a topological operator that modifies one polyhedron into another. It is similar to expansion: it moves the faces apart (outward), and adds a new face between each two adjacent faces; but contrary to expansion, it maintains the original vertices. (Equivalently: it separates the faces by reducing them ...

  4. Chamfered dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Chamfered_dodecahedron

    It is constructed as a chamfer (edge-truncation) of a regular dodecahedron. The pentagons are reduced in size and new hexagonal faces are added in place of all the original edges. Its dual is the pentakis icosidodecahedron. It is also called a truncated rhombic triacontahedron, constructed as a truncation of the rhombic triacontahedron.

  5. Truncated dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Truncated_dodecahedron

    The truncated dodecahedron is constructed from a regular dodecahedron by cutting all of its vertices off, a process known as truncation. [1] Alternatively, the truncated dodecahedron can be constructed by expansion: pushing away the edges of a regular dodecahedron, forming the pentagonal faces into decagonal faces, as well as the vertices into triangles. [2]

  6. Cantellation (geometry) - Wikipedia

    en.wikipedia.org/wiki/Cantellation_(geometry)

    In geometry, a cantellation is a 2nd-order truncation in any dimension that bevels a regular polytope at its edges and at its vertices, creating a new facet in place of each edge and of each vertex. Cantellation also applies to regular tilings and honeycombs .

  7. Truncated 8-simplexes - Wikipedia

    en.wikipedia.org/wiki/Truncated_8-simplexes

    In eight-dimensional geometry, a truncated 8-simplex is a convex uniform 8-polytope, being a truncation of the regular 8-simplex. There are four unique degrees of truncation. Vertices of the truncation 8-simplex are located as pairs on the edge of the 8-simplex. Vertices of the bitruncated 8-simplex are located on the triangular faces of the 8 ...

  8. Truncated cube - Wikipedia

    en.wikipedia.org/wiki/Truncated_cube

    3D model of a truncated cube. In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid.It has 14 regular faces (6 octagonal and 8 triangular), 36 edges, and 24 vertices.

  9. Icosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Icosidodecahedron

    The icosidodecahedron is a rectified dodecahedron and also a rectified icosahedron, existing as the full-edge truncation between these regular solids. The icosidodecahedron contains 12 pentagons of the dodecahedron and 20 triangles of the icosahedron :