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 Geometric Formulas (Ask Dr. Math FAQ) - Math Forum Formulas for two-dimensional figures: triangle (equilateral, isosceles, right, scalene); quadrilateral (general, square, rectangle, parallelogram, rhombus, trapezoid, kite, cyclic and cyclic-inscriptable); regular polygon; circle (arc, segment, sector); ellipse; parabolic segment; and three-dimensional figures: rectangular parallelepiped (cube); prism; pyramid (square pyramid, frustum); regular polyhedron (tetrahedron, cube, octahedron, dodecahedron, icosahedron); cylinder (right circular); cone (right circular, frustum); sphere (sector, cap, segment, zone, lune); ellipsoid; circular torus; spherical polygon. Includes Defining Geometric Figures. more>> Naming Polygons and Polyhedra - Math Forum, Ask Dr. Math FAQ What do you call an 11-sided polygon? A 14-sided polygon? Is there a list of names of polygons? What about polyhedra? more>> Polyhedra Study - Ha Le An attempt to bring out the beauty of polyhedral study in particular and of mathematics in general via the use of the geom3d package in Maple and VRML (Virtual Reality Modelling Language). Categories: regular polyhedra; Archimedean solids; duality; facet; stellate; transformation. more>> Prism Formulas (Ask Dr. Math FAQ) - Math Forum Formulas for finding the surface area and volume of a prism. more>> Rectangular Parallelepiped, Cube Formulas (Ask Dr. Math FAQ) - Math Forum Formulas for finding the surface area and volume of a rectangular parallelepiped and a cube. more>> Regular Polyhedra: Formulas (Ask Dr. Math FAQ) - Math Forum Formulas for finding the surface area, perimeter, volume, etc. of regular polyhedra: tetrahedron, cube, octahedron, dodecahedron, icosahedron. more>> Studying Polyhedra - Suzanne Alejandre What is a polyhedron? A definition and a Java applet to help in exploring the five regular polyhedra to find how many faces and vertices each has, and what polygons make up the faces. Also links to a page of information about buckyballs, stories written by students after studying polyhedra, other sites with information about regular polyhedra, and other sites with information about Greece and Greek mathematicians. more>> The Uniform Polyhedra - Roman Maeder A shortened version of the notebook Polyhedra.ma from Illustrated Mathematics [Gloor/Amrhein/Maeder95]. Uniform polyhedra have regular faces and congruent vertices. Allowing for non-convex faces and vertex figures, there are 75 such polyhedra, as well as 2 infinite families of prisms and antiprisms. A recently discovered uniform way of computing their vertex coordinates is the basis for a program to display all of these solids. The metric properties and graphics data were computed with a Mathematica program, available from this site. Graphics include a list and thumbnail pictures of all uniform polyhedra; a visual index (sensitive map) of all 80 polyhedra; a list sorted by Wythoff symbol; and a guided tour. more>> Virtual Polyhedra - George W. Hart A growing collection of over 1000 virtual reality polyhedra to explore, complementing Hart's Pavilion of Polyhedreality. Includes instructions for building paper models of polyhedra including modular origami, with ideas for classroom use. Each of the sections contains background information and exercises, a list of virtual reality models, and links to further topics. Platonic Solids (Regular Convex Polyhedra); Kepler-Poinsot Polyhedra (Regular NonConvex Polyhedra); Archimedean Polyhedra (Semi-Regular Convex Polyhedra); Prisms and Anti-Prisms; Archimedean Duals; Quasi-Regular Polyhedra; Johnson Solids (the remaining convex polyhedra with regular faces); Pyramids, Dipyramids, and Trapezohedra; Compound Polyhedra - Introduction; Stellated Polyhedra - Introduction; Compounds of Cubes; Convex Deltahedra; Zonohedra; Uniform Polyhedra; Uniform Compounds of Uniform Polyhedra; Stellations of the Icosahedron; Stellations of the Rhombic Triacontahedron; Other Good Stuff: Alphabetic list of articles, Alphabetic listing of all the polyhedra models, a Glossary, and an Annotated Bibliography. Also background material on polygons and on polyhedron names. more>>
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