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If a plane intersects a solid (a 3-dimensional object), then the region common to the plane and the solid is called a cross-section of the solid. [1] A plane containing a cross-section of the solid may be referred to as a cutting plane. The shape of the cross-section of a solid may depend upon the orientation of the cutting plane to the solid.
The rhombic dodecahedron forms the maximal cross-section of a 24-cell, and also forms the hull of its vertex-first parallel projection into three dimensions. The rhombic dodecahedron can be decomposed into six congruent (but non-regular) square dipyramids meeting at a single vertex in the center; these form the images of six pairs of the 24 ...
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.
The diagram is named for Victor Schlegel, who in 1886 introduced this tool for studying combinatorial and topological properties of polytopes. In dimension 3, a Schlegel diagram is a projection of a polyhedron into a plane figure; in dimension 4, it is a projection of a 4-polytope to 3-space.
This is left blank for non-orientable polyhedra and hemipolyhedra (polyhedra with faces passing through their centers), for which the density is not well-defined. Note on Vertex figure images: The white polygon lines represent the "vertex figure" polygon. The colored faces are included on the vertex figure images help see their relations.
A section, or cross-section, is a view of a 3-dimensional object from the position of a plane through the object. A section is a common method of depicting the internal arrangement of a 3-dimensional object in two dimensions. It is often used in technical drawing and is traditionally crosshatched. The style of crosshatching often indicates the ...
In geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U 67. It has 62 faces (20 triangles, 30 squares and 12 pentagrams), 120 edges, and 60 vertices. [1] It is also called the quasirhombicosidodecahedron. It is given a Schläfli symbol rr{5 ⁄ 3,3}. Its vertex figure is a crossed quadrilateral.
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. The term "polyhedron" may refer either to a solid figure or to its boundary surface.