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Peak, an (n-3)-dimensional element 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.
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 ).
The Platonic solids have been known since antiquity. It has been suggested that certain carved stone balls created by the late Neolithic people of Scotland represent these shapes; however, these balls have rounded knobs rather than being polyhedral, the numbers of knobs frequently differed from the numbers of vertices of the Platonic solids, there is no ball whose knobs match the 20 vertices ...
The (n − 3)-faces of an n-polytope are called peaks. A peak contains a rotational axis of facets and ridges in a regular polytope or honeycomb. For example: The peaks of a 3D polyhedron or plane tiling are its 0-faces or vertices. The peaks of a 4D polytope or 3-honeycomb are its 1-faces or edges.
A representation of a three-dimensional Cartesian coordinate system. In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point.
In geometry, shape excludes information about the object's position, size, orientation and chirality. [1] A figure is a representation including both shape and size (as in, e.g., figure of the Earth). A plane shape or plane figure is constrained to lie on a plane, in contrast to solid 3D shapes.
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