 Plato's Molecule  Ivars Peterson (MathTrek)
In his dialogue Timaeus, the Greek philosopher Plato (427347 B.C.) carefully laid out his reasoning for ascribing certain geometric shapes to the minuscule particles that constituted the four elements of matter. In his view, these elements  fire, air,
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 Poly and Poly Pro  Pedagoguery Software
Mac and Windows shareware programs for exploring and constructing paper models of polyhedra. With Poly, you can manipulate a polyhedral solid on the computer and print out a flattened version (a net) which can then be cut out, folded, and taped, to produce
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 Polydron
British vendors of two and three dimensional, handson, geometric modelling systems and other geometric toys. Polydron Corporation history, online catalogue, and order form. To purchase Polydron products in the United States, contact Polydron International
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 Polyedergarten  U. Mikloweit
Photographs of paper models of uniform polyhedra, prisms and compounds. Versions of the site also exist in German and French.
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 Polygons, Polyhedra, Polytopes  Russell Towle
Polytope is the general term of the sequence, point, segment, polygon,
polyhedron, ... . Towle offers several pages devoted to the theory of polytopes, from polygons to star polytopes in 4space, including Mathematica notebooks with constructions.
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 Polyhedra and Polytopes (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on geometric properties of polygons, polyhedra, and higher dimensional polytopes (particularly convex polytopes).
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 Polyhedra Collection  V. Bulatov
Galleries of polyhedra shown using JPEG pictures and 3D objects in VRML2.0 format. Uniform polyhedra; Duals; Compounds; Johnson's solids; 59 stellations of icosahedron; 270 stellations of deformed dodecahedron; symmetric stellations of rhombic triacontahedron:
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 Polyhedra (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
A polyhedron is the threedimensional version of a polygon, a threedimensional figure made by gluing polygons together. This handout discusses polyhedra, presents explorative activities, and supplies a "homework" assignment. Includes the first 20 Greek
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 Polyhedra in the Classroom  Suzanne Alejandre
Middle School student activities to pursue with a computer in the classroom. Introduction to Polyhedra; paper nets to print out and fold; Kaleidotile; Buckyballs; Crystals (paper nets, systems); Cube coloring problems; links to polyhedra on the Web.
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 Polyhedral Solids  Tom Gettys
The study of polyhedra is one of those special areas of Mathematics which allow the amateur and expert to work with an equal delight. The Platonic Solids; The Archimedean Solids; The KeplerPoinsot Polyhedra; Compound Solids; Stellated Polyhedra. See
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 Polyhedra  Peter Cromwell
Ancient manuscripts from Egypt and China relate ideas concerning the calculation of the volumes of polyhedra, while the Greek tradition of geometry gave us the construction of the regular polyhedra or Platonic solids. In modern times, polyhedra and their
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 Polyhedra plaited with paper strips  H. B. Meyer
A guide to generating certain polyhedra (Platonian, Archimedian and other solids) by plaiting paper strips (glueless method). In several cases pattern download of the paper strips is possible. In German and English.
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 Polyhedra  Rolf Asmund
A gallery of regular polyhedra, snub uniform polyhedra, deltahedra (polyhedra consisting only of equilateral triangles), and polychora; with animations, still graphics, and some taxonomic data (vertices, edges, faces, polygons, radii, and more). Mobius
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 Polyhedra Sketches  Bill Finzer, Key Curriculum Press
Sketches showing the platonic solids in true perspective. You have control over the placement of the picture plane, the station point, and the horizon. An animation button rotates the figure. Some of the sketches show in 3D if you have a pair of 3D glasses.
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 Polyhedron: An application in solid geometry  Stelian Dumitrascu
Software based on "deductionfree geometry," which allows the user to perform various actions upon solids as if holding these solids in your hands. It simulates a number of tools, such as the ruler, protractor, setsquare, compass, bisector, saw, and eraser.
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 Polyhedrons: PolyMod Polyhedron Modeler  Daniel Grunberg
An experimental K12 and collegelevel Windows software program that allows the user to create both regular and irregular 3dimensional polyhedrons on the screen and view them from different angles, then print out a polyhedral net or template and glue
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 Polymorf  Rick Engel
A math manipulative, construction set toy, model building kit, and 3D puzzle all in one, used for modeling polyhedra and the structure of molecules and crystals. Build lifelike geometric models of creatures, vehicles, and structures. For all ages.
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 Polyominoes  Kevin Gong
Information and Polyominoes software to download. A polyomino is a piece made up entirely of squares connected edgetoedge. For example, a domino is a polyomino with 2 squares. In this program, you can use pentominoes, tetrominoes, trominoes, hexominoes,
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 Polytopes, Zonohedra, Zonotiles, Mathematica notebooks  Russell Towle
Some of the author's endeavors in geometry, including studies of zonohedra, polyhedra, spacefillings, polytopes in higher space, and the discovery of new types of polyhedra and spacefillers. Mathematica notebooks are provided which create these kinds
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 Praktick  Praktick Learning private Ltd.
Autoscoring practice problems aligned to the UK's Central Board of Secondary Education (CBSE) Standards, from prekindergarten to grade seven. Questions adjust dynamically based on performance, while a timer counts up response time; incorrect answers
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 Productive Struggle
Group blog, with most contributions by secondary math and science teachers, that aims to "push teachers to learn in the same way that we push our students to learn" and "work together to make our struggles productive." Posts, which date back to March,
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 Professors Rethinking Options in Mathematics for Prospective Teachers (PROMPT)  Humboldt State University Mathematics Department
A program funded by the National Science Foundation to bring together mathematics faculty members from across the country to explore the question, "How can we prepare elementary school teachers to teach for the future rather than the past?" The purpose
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 Punctured Polyhedra  Ivars Peterson (MathTrek)
A tetrahedron has four triangular faces, four vertices, and six edges. When a vertex of one tetrahedron pierces the face of a second tetrahedron it forms a new, more complicated polyhedron: one triangular face has a triangular "hole" where the face was
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 Puzzles  Martin Watson
Blogs, comments, musings, design sketches, and photographs of mechanical puzzles by an avid collector and craftsman. Puzzle news, the author's own burrs (Watson's wormhole, digigrams, Dutch cubist), indepth explorations of manipulative puzzles (Puzzles
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 the radical rational ...  Pam Wilson
Blog by a National Board Certified Teacher (NBCT) of Algebra II and Geometry "in search of innovative ideas with a wellbalanced approach for the math classroom." Posts, which date back to July, 2011, have included "The Purpose of Life and The Quadratic
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 Recreational Mathematics Topics  Steven Dutch; University of Wisconsin  Green Bay
Contents: Symmetry, Crystals, Polyhedra and Tilings: an extensive, illustrated collection including reflectional and rotational symmetry; repeating patterns in two and three dimensions; building crystal forms with unit cells; regular, Archimedean, radial,
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 Rectilinear Geometry (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on geometric problems defined on squares and rectangles, higher dimensional boxes, cubes, and hypercubes, right triangles and other rightangled figures, and "taxicab geometry" in which distances are measured
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 Regular Solids  Jim Loy
An elementary introduction to regular polyhedra, solid geometric figures with identical regular polygons as their faces and the same number of faces meeting at every corner (vertex).
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 Rhombic Dodecahedron: Hidden Within or Surrounding the Cube?  Joyce Frost, Kris Koch, Park City Mathematics Institute
This activity illustrates the interconnections between a cube and a rhombic dodecahedron, using a Zome Tool or drinking straws and ribbons. One of the PCMI Resources for Teachers.
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 Robert Kaplinsky  Glenrock Consulting  Robert Kaplinsky
Lessons consist of "The Challenge(s)," "Question(s) To Ask," "Consider This," and alignments to Common Core State Standards (CCSS): "How Can We Water All Of The Grass?" and "How Much Money Should Dr. Evil Demand?" and "How Did They Make Ms. PacMan?"
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 Rubik's Cube Information  Michael Reid
All about Rubik's Cube  even a mailing list. Site contents include: the Nederlandse Kubus Club; Rubik's cube pages on the Web; Cube books; Sources of cubelike puzzles; the author's notes, including an optimal cube solver; other Cube solutions on the
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 Rubik's Cube Java Applet  Michael Schubart
To twist the cube, press the mouse button over a cubelet face that belongs to the slice you want to move. Keeping the button pressed, drag the mouse in the desired direction; then release the button. Moving the whole cube is done in the same way  just
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 Rubik's Games  Androsoft
Dedicated to the first PC CDROM game from Erno Rubik, Rubik's Games contains 5 subgames: Rubik's Classic, Cover Up, Paint War, Rubik's Playground and ZigThrough. Download the Rubik's Games Web Site Plugin plugin or a demo of the Rubik's Game CDROM.
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 Rubik's Online  Rubik/Seven Towns
The official online site for the Rubik's cube. Play with the cube and other Rubik's games and puzzles online; find information on where to buy Rubik's products; use the forum to exchange views, opinions, comments, suggestions and anecdotes related to
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 Rubix Corner  Duane Cash
The site includes information regarding the Duane Cash Cube Collection now featured at Hessport's Rubikshop in their "collectibles" section. New puzzles include the Rubik's Triamese, Fusion, Fusion+, SpeedFusion, 5x3, and 4x3 Cubes, which give those interested
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 Selected Recent Publications  George W. Hart
Areas of Hart's research and pointers to further information, including a bibliography of his publications. Links to pages on: Multidimensional Analysis; Nonintrusive Appliance Load Monitoring; Telecommunications Network Management; Viterbi Algorithm
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 SketchMad  Nathalie Sinclair
An archived resource, not currently updated: A resource center devoted to using The Geometer's Sketchpad in the classroom. Includes tips, strategies, lesson plans, and sketches for beginning and intermediate Sketchpad teachers, stories from the classroom
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 Solids Workshop  FacticsMax
A program that allows you to select a square, triangular, pentagonal, or hexagonal prism, pyramid, or frustum; or a cylinder or cone, choose the height, side, (and frustum height) you desire, and print out a net pattern that will fold up into the selected
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 Solving Rubik's Cube  David Lee Winston Miller
A "bestfast" Arity Prolog program and demonstration of an efficient heuristic search method to solve Rubik's Cube. Examine the cube's topography (its flat layout) and "submachines." Documentation includes "Understanding the problem," "Why this approach
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 Solving the Rubik's Cube  Matthew Monroe
Instructions, popularized by Minh Thai, the National Champion cube solver, for solving a 3x3x3 Rubik's Cube. Also, instructions for how to solve a cube when it has oriented pictures on each face. Directions for solving a 2x2x2 Rubik's mini cube, the professor
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 The Soma Cube Puzzle  Modvix
Purchase the Soma Cube. Piet Hein, a Danish poet and inventor, visualized the set of all irregular shapes formed by no more than 4 cubes, each of the same size, and realized that the seven simplest irregular combinations of cubes can form a larger Soma
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 Some Solid (Threedimensional) Geometrical Facts about the Golden Section  Ron Knott
Phi and threedimensional geometry  Dice Shapes; Coordinates and other statistics of the 5 Platonic Solids; The Greeks and the platonic solids; Quasicrystals and Phi; Footnotes on Plato and Euclid, and on shapes for fair dice.
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 sonata mathematique  Rachel Kernodle
Blog by a high school math and learning specialist. Posts, which date back to June, 2011, have included "twitter math camp," "mathematical art," "i also want you to learn…," and "rational functions take two."
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 SpaceBric
Tetrahedral linking blocks and design software using that shape. Download trial versions of the software or get the fullyfeatured versions with a registration key. Blocks may be purchased on line as well. SpaceBric also offers school fundraising and
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 SpaceShape  Matt Storz
SpaceShape is a Windows95 program that allows various 3D shapes to be created and then flattened so that a pattern can be printed to make a model of the 3D shape. Various 3D shapes are supplied with the program (octahedron, dodecahedron, icosahedron,
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 Spidron System  Daniel Erdely
Erdely calls a planar, planefilling object a Spidron. Upon threedimensional deformation subject to specific constraints, the planar system generates a regular, dynamic, geometrical construction. Erdely's experiments have led to the idea of creating
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 Stella: Polyhedron Navigator  Robert Webb
"Small Stella" is a program for viewing polyhedra and printing their nets so you can build your own. It has over 150 builtin models, plus their duals. Models include Platonic solids, Archimedean, KeplerPoinsot, Johnson solids, "Near Misses," and Stewart
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 Stellated Icosahedra  Roman Maeder
An excerpt of an article published in Mathematica in Education. There are 59 stellations of the icosahedron; these pages contain various images of them, ordered by increasing circumradius, and some background information. The metric properties and graphics
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 studio:ludens  Wouter Walmink and Alexander Rulkens
Free online tools that "let you play with your own creativity," designed by two Dutch industrial and interaction designers in Eindhoven. Create your own patterns with Repper; your own tessellating coasters with Epa:kato; your own fractals and other complex
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 studymaths.co.uk  Jonathan Hall
Free help on your maths questions. See also the bank of autoscoring GCSE maths questions, games, and resources such as revision notes, interactive formulae, and glossary of terms.
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