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  2. Square pyramid - Wikipedia

    en.wikipedia.org/wiki/Square_pyramid

    A polyhedron's surface area is the sum of the areas of its faces. The surface area of a right square pyramid can be expressed as = +, where and are the areas of one of its triangles and its base, respectively. The area of a triangle is half of the product of its base and side, with the area of a square being the length of the side squared.

  3. Surface area - Wikipedia

    en.wikipedia.org/wiki/Surface_area

    A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...

  4. Cubic pyramid - Wikipedia

    en.wikipedia.org/wiki/Cubic_pyramid

    In 4-dimensional geometry, the cubic pyramid is bounded by one cube on the base and 6 square pyramid cells which meet at the apex. Since a cube has a circumradius divided by edge length less than one, [ 1 ] the square pyramids can be made with regular faces by computing the appropriate height.

  5. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    5-cube, Rectified 5-cube, 5-cube, Truncated 5-cube, Cantellated 5-cube, Runcinated 5-cube, Stericated 5-cube; 5-orthoplex, Rectified 5-orthoplex, Truncated 5-orthoplex, Cantellated 5-orthoplex, Runcinated 5-orthoplex; Prismatic uniform 5-polytope For each polytope of dimension n, there is a prism of dimension n+1. [citation needed]

  6. Rhombic dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombic_dodecahedron

    For example, with 4 square faces, and 60-degree rhombic faces, and D 4h dihedral symmetry, order 16. It can be seen as a cuboctahedron with square pyramids attached on the top and bottom. In 1960, Stanko Bilinski discovered a second rhombic dodecahedron with 12 congruent rhombus faces, the Bilinski dodecahedron. It has the same topology but ...

  7. Solid geometry - Wikipedia

    en.wikipedia.org/wiki/Solid_geometry

    Hyperboloid of one sheet. Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space). [1] 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.

  8. Cube - Wikipedia

    en.wikipedia.org/wiki/Cube

    The cube is non-composite polyhedron, meaning it is a convex polyhedron that cannot be separated into two or more regular polyhedrons. The cube can be applied to construct a new convex polyhedron by attaching another. [40] Attaching a square pyramid to each square face of a cube produces its Kleetope, a polyhedron known as the tetrakis ...

  9. Close-packing of equal spheres - Wikipedia

    en.wikipedia.org/wiki/Close-packing_of_equal_spheres

    [1] [2] Highest density is known only for 1, 2, 3, 8, and 24 dimensions. [3] Many crystal structures are based on a close-packing of a single kind of atom, or a close-packing of large ions with smaller ions filling the spaces between them. The cubic and hexagonal arrangements are very close to one another in energy, and it may be difficult to ...

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