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Prismatoid with parallel faces A 1 and A 3, midway cross-section A 2, and height h. In geometry, a prismatoid is a polyhedron whose vertices all lie in two parallel planes.Its lateral faces can be trapezoids or triangles. [1]
A central cross section of a regular tetrahedron is a square. The two skew perpendicular opposite edges of a regular tetrahedron define a set of parallel planes. When one of these planes intersects the tetrahedron the resulting cross section is a rectangle. [11] When the intersecting plane is near one of the edges the rectangle is long and skinny.
Colored regions are cross-sections of the solid cone. Their boundaries (in black) are the named plane sections. A cross section of a polyhedron is a polygon. The conic sections – circles, ellipses, parabolas, and hyperbolas – are plane sections of a cone with the cutting planes at various different angles, as seen in the diagram at left.
In geometry, the regular icosahedron (or simply icosahedron) is a convex polyhedron that can be constructed from pentagonal antiprism by attaching two pentagonal pyramids with regular faces to each of its pentagonal faces, or by putting points onto the cube. The resulting polyhedron has 20 equilateral triangles as
A pyramid is a polyhedron that may be formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form an isosceles triangle called a lateral face. [7] The edges connected from the polygonal base's vertices to the apex are called lateral edges. [8]
The geodesic distance between any two points on the surface of a polyhedron measures the length of the shortest curve that connects the two points, remaining within the surface. By Alexandrov's uniqueness theorem , every convex polyhedron is uniquely determined by the metric space of geodesic distances on its surface.
When two cells in the Voronoi diagram share a boundary, it is a line segment, ray, or line, consisting of all the points in the plane that are equidistant to their two nearest sites. The vertices of the diagram, where three or more of these boundaries meet, are the points that have three or more equally distant nearest sites.
It has 24 edges, and 14 vertices of 2 types. As a Catalan solid, it is the dual polyhedron of the cuboctahedron. As a parallelohedron, the rhombic dodecahedron can be used to tesselate its copies in space creating a rhombic dodecahedral honeycomb. There are some variations of the rhombic dodecahedron, one of which is the Bilinski dodecahedron.