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The 600-cell is the fifth in the sequence of 6 convex regular 4-polytopes (in order of complexity and size at the same radius). [a] It can be deconstructed into twenty-five overlapping instances of its immediate predecessor the 24-cell, [5] as the 24-cell can be deconstructed into three overlapping instances of its predecessor the tesseract (8-cell), and the 8-cell can be deconstructed into ...
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. For instance, while all the cross-sections of a ball are disks, [2] the cross-sections of a cube depend on how the cutting plane is related to the ...
The resulting polyhedron has 20 equilateral triangles as its faces, 30 edges, and 12 vertices. It is an example of a Platonic solid and of a deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron. Many polyhedra are constructed from the regular icosahedron.
The solid angle of a latitude-longitude rectangle on a globe is ( ) (), where φ N and φ S are north and south lines of latitude (measured from the equator in radians with angle increasing northward), and θ E and θ W are east and west lines of longitude (where the angle in radians increases eastward). [10]
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.
Elongated indicates a prism is joined to the base of the solid, or between the bases; gyroelongated indicates an antiprism. Augmented indicates another polyhedron, namely a pyramid or cupola, is joined to one or more faces of the solid in question. Diminished indicates a pyramid or cupola is removed from one or more faces of the solid in question.
Section 8 is the central section, the largest hull, with the same radius as the 120-cell. Except for the central section 8, the sections occur in parallel pairs, on either side of the central section. Hull 8 is dimensionally analogous to the equator, while hulls 1 - 7 are dimensionally analogous to lines of latitude.
A polyhedron comprising an n-sided polygonal base, a second base translated and rotated.sides]] of the two bases square antiprism: Bipyramid: A polyhedron comprising an n-sided polygonal center with two apexes. triangular bipyramid: Trapezohedron: A polyhedron with 2n kite faces around an axis, with half offsets tetragonal trapezohedron: Cone