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  2. Edge (geometry) - Wikipedia

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

    In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. [1] In a polygon, an edge is a line segment on the boundary, [2] and is often called a polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides ...

  3. List of small polyhedra by vertex count - Wikipedia

    en.wikipedia.org/wiki/List_of_small_polyhedra_by...

    The smallest polyhedron is the tetrahedron with 4 triangular faces, 6 edges, and 4 vertices. Named polyhedra primarily come from the families of platonic solids, Archimedean solids, Catalan solids, and Johnson solids, as well as dihedral symmetry families including the pyramids, bipyramids, prisms, antiprisms, and trapezohedrons.

  4. Polyhedron - Wikipedia

    en.wikipedia.org/wiki/Polyhedron

    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.

  5. Szilassi polyhedron - Wikipedia

    en.wikipedia.org/wiki/Szilassi_polyhedron

    The tetrahedron and the Szilassi polyhedron are the only two known polyhedra in which each face shares an edge with each other face.. If a polyhedron with f faces is embedded onto a surface with h holes, in such a way that each face shares an edge with each other face, it follows by some manipulation of the Euler characteristic that

  6. Table of polyhedron dihedral angles - Wikipedia

    en.wikipedia.org/wiki/Table_of_polyhedron...

    Duals of the ditrigonal polyhedra Small triambic icosahedron (Dual of small ditrigonal icosidodecahedron) — V(3. ⁠ 5 / 2 ⁠.3. ⁠ 5 / 2 ⁠.3. ⁠ 5 / 2 ⁠) Medial triambic icosahedron (Dual of ditrigonal dodecadodecahedron) — V(5. ⁠ 5 / 3 ⁠.5. ⁠ 5 / 3 ⁠.5. ⁠ 5 / 3 ⁠) Great triambic icosahedron (Dual of great ditrigonal ...

  7. Polyhedral graph - Wikipedia

    en.wikipedia.org/wiki/Polyhedral_graph

    A polyhedral graph is the graph of a simple polyhedron if it is cubic (every vertex has three edges), and it is the graph of a simplicial polyhedron if it is a maximal planar graph. For example, the tetrahedral, cubical, and dodecahedral graphs are simple; the tetrahedral, octahedral, and icosahedral graphs are simplicial.

  8. Wedge (geometry) - Wikipedia

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

    A wedge is a polyhedron of a rectangular base, with the faces are two isosceles triangles and two trapezoids that meet at the top of an edge. [1]. A prismatoid is defined as a polyhedron where its vertices lie on two parallel planes, with its lateral faces are triangles, trapezoids, and parallelograms; [2] the wedge is an example of prismatoid because of its top edge is parallel to the ...

  9. Archimedean solid - Wikipedia

    en.wikipedia.org/wiki/Archimedean_solid

    Archimedean Solids at Visual Polyhedra by David I. McCooey; Virtual Reality Polyhedra, The Encyclopedia of Polyhedra by George W. Hart; Penultimate Modular Origami by James S. Plank; Interactive 3D polyhedra in Java; Solid Body Viewer is an interactive 3D polyhedron viewer which allows you to save the model in svg, stl or obj format.

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