Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space). The Britannica Guide to Geometry, Britannica Educational Publishing, 2010, pp. 67–68. 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 of of various solids, including pyramids, prisms (and other polyhedrons), cubes, cylinders, cones (and Frustum)..
Advanced topics include:
+ Major types of shapes that either constitute or define a volume. ! Figure !! Definitions !! colspan=2 | Images | ||
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Polyhedron | Flat faces, straight edges and sharp corners or vertices | Small stellated dodecahedron | Toroidal polyhedron |
Uniform polyhedron | as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other) | (Regular) Tetrahedron and Cube | Uniform Snub dodecahedron |
A polyhedron comprising an n-sided base and a vertex point | square pyramid | ||
A polyhedron comprising an n-sided base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all ) joining corresponding sides of the two bases | hexagonal prism | ||
A polyhedron comprising an n-sided base, a second base translated and rotated.sides]] of the two bases | square antiprism | ||
A polyhedron comprising an n-sided center with two apexes. | triangular bipyramid | ||
A polyhedron with 2 n kite faces around an axis, with half offsets | tetragonal trapezohedron | ||
Cone | Tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex | A right circular cone and an oblique circular cone | |
Cylinder | Straight parallel sides and a circular or oval cross section | A solid elliptic cylinder | A right and an oblique circular cylinder |
Ellipsoid | A surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation | Examples of ellipsoids | sphere (top, a=b=c=4), spheroid (bottom left, a=b=5, c=3), tri-axial ellipsoid (bottom right, a=4.5, b=6, c=3)]] |
Lemon | A lens (or less than half of a circular arc) rotated about an axis passing through the endpoints of the lens (or arc) | ||
Hyperboloid | A surface that is generated by rotating a hyperbola around one of its principal axes |
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