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The boundary of a cross-section in three-dimensional space that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space ...
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.
For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure : not itself an element of a polytope, but a diagram showing how the elements meet.
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]
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.
A polyhedron is said to be convex if a line between any two of its vertices lies either within its interior or on its boundary, and additionally, if no two faces are coplanar (lying in the same plane) and no two edges are collinear (segments of the same line). [2] Of the eight convex deltahedra, three are Platonic solids and five are Johnson ...
where V, E, and F are respectively the numbers of vertices (corners), edges and faces in the given polyhedron. [2] Any convex polyhedron's surface has Euler characteristic = + = . This equation, stated by Euler in 1758, [3] is known as Euler's polyhedron formula. [4]
A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball consists of a sphere and its interior. Solid geometry deals with the measurements of volumes of various solids, including pyramids , prisms (and other polyhedrons ), cubes , cylinders , cones (and truncated cones ).