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  2. Cube - Wikipedia

    en.wikipedia.org/wiki/Cube

    t. e. In geometry, a cube or regular hexahedron is a three-dimensional solid object bounded by six congruent square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It is a type of parallelepiped, with pairs of parallel opposite faces, and more specifically a rhombohedron, with congruent edges, and a rectangular ...

  3. Tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Tetrahedron

    Tetrahedron. In geometry, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices. The tetrahedron is the simplest of all the ordinary convex polyhedra.

  4. Platonic solid - Wikipedia

    en.wikipedia.org/wiki/Platonic_solid

    Platonic solid. In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex.

  5. Face (geometry) - Wikipedia

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

    In elementary geometry, a face is a polygon [note 1] on the boundary of a polyhedron. [3][4] Other names for a polygonal face include polyhedron side and Euclidean plane tile. For example, any of the six squares that bound a cube is a face of the cube. Sometimes "face" is also used to refer to the 2-dimensional features of a 4-polytope.

  6. Polyhedron - Wikipedia

    en.wikipedia.org/wiki/Polyhedron

    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.

  7. Cuboid - Wikipedia

    en.wikipedia.org/wiki/Cuboid

    Cuboid. In geometry, a cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six faces; it has eight vertices and twelve edges. A rectangular cuboid (sometimes also called a "cuboid") has all right angles and equal opposite faces. Etymologically, "cuboid" means "like a cube ", in the sense of a convex solid which can ...

  8. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms have either regular star polygon faces or vertex figures or both. This list includes these: one degenerate polyhedron, Skilling's figure with overlapping edges. It was proven in Sopov (1970) that there are only 75 uniform polyhedra ...

  9. Regular polyhedron - Wikipedia

    en.wikipedia.org/wiki/Regular_polyhedron

    Regular polyhedron. A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent definitions are used; a common one is that the faces are congruent regular ...