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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 5 Platonic solids are called a tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron with 4, 6, 8, 12, and 20 sides respectively. The regular hexahedron is a cube . Table of polyhedra
In geometry, the Rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges.
Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.
Lists of shapes cover different types of geometric shape and related topics. They include mathematics topics and other lists of shapes, such as shapes used by drawing or teaching tools. They include mathematics topics and other lists of shapes, such as shapes used by drawing or teaching tools.
Stones carved in shapes resembling clusters of spheres or knobs have been found in Scotland and may be as much as 4,000 years old. Some of these stones show not only the symmetries of the five Platonic solids, but also some of the relations of duality amongst them (that is, that the centres of the faces of the cube gives the vertices of an ...
The above shapes may also be realized as slices orthogonal to the long diagonal of a tesseract. If this diagonal is oriented vertically with a height of 1, then the first five slices above occur at heights r , 3 / 8 , 1 / 2 , 5 / 8 , and s , where r is any number in the range 0 < r ≤ 1 / 4 , and s is any number ...
Platonic solid: Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron; Regular spherical polyhedron. Dihedron, Hosohedron; Kepler–Poinsot polyhedron (Regular star polyhedra) Small stellated dodecahedron, Great stellated dodecahedron, Great icosahedron, Great dodecahedron; Abstract regular polyhedra (Projective polyhedron)