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Octahedral (red) and tetrahedral (blue) interstitial symmetry polyhedra in a face-centered cubic lattice. The actual interstitial atom would ideally be in the middle of one of the polyhedra. A close packed unit cell, both face-centered cubic and hexagonal close packed, can form two different shaped holes.
Rather than adopting structures based on deltahedra, the 5n-type clusters have structures based on a different series of polyhedra known as the 3-connected polyhedra, in which each vertex is connected to 3 other vertices. The 3-connected polyhedra are the duals of the deltahedra. The common types of 3-connected polyhedra are listed below.
This is an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger. The book was written as a guide book to building polyhedra as physical models. It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes.
Interstitial atoms (blue) occupy some of the spaces within a lattice of larger atoms (red) In materials science, an interstitial defect is a type of point crystallographic defect where an atom of the same or of a different type, occupies an interstitial site in the crystal structure.
In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many' and ἕδρον (-hedron) 'base, seat') is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is a polyhedron that bounds a convex set.
An n-dimensional polyhedron is a geometric object that generalizes the 3-dimensional polyhedron to an n-dimensional space. It is defined as a set of points in real affine (or Euclidean) space of any dimension n, that has flat sides. It may alternatively be defined as the intersection of finitely many half-spaces. Unlike a 3-dimensional ...
A convex polyhedron whose faces are regular polygons is known as a Johnson solid, or sometimes as a Johnson–Zalgaller solid [3]. Some authors exclude uniform polyhedra from the definition. A uniform polyhedron is a polyhedron in which the faces are regular and they are isogonal ; examples include Platonic and Archimedean solids as well as ...
The dual of a non-convex polyhedron is also a non-convex polyhedron. [2] ( By contraposition.) There are ten non-convex isotoxal polyhedra based on the quasiregular octahedron, cuboctahedron, and icosidodecahedron: the five (quasiregular) hemipolyhedra based on the quasiregular octahedron, cuboctahedron, and icosidodecahedron, and their five (infinite) duals: