Zvi Har'El I am a senior lecturer in the Department of Mathematics at the Technion, Israel Institute of Technology. I have been here since 1978, after spending two years in the University of Illinois, Urbana, IL. Later, I spent two more years in Bell Labs, Murray Hill, NJ, and three semesters in IBM Research Lab in Haifa. I am married to Zahava, and have three children: Nadav, Gilead ...

Various resources regarding virtual reality polyhedra.

Pedagoguery Software Inc. Die-Cast Metal Models Mathematics Software GRAFEQ Poly Download Register Included Polyhedra Poly Pro Tess Mathematics Tokens Models Posters T-Shirts GIF Software A Smaller GIF COGS GifgIfgiF itsagif Free Software iTime NETime Contact Information Email Policy Poly is a shareware program for exploring and constructing polyhedra. With Poly, you can manipulate polyhedral ...

The Uniform Polyhedra Contents Introduction About the Images on These Pages Background Information The Wythoff Symbol Geometric Properties Introduction Uniform polyhedra consist of 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 ...

Paper models: Platonic solids, Archemedean solids and other polyhedra ...

The Math Forum's Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites relating to Polyhedra.

Jim Plank's Origami Page (Modular) Instructions Directions for making polyhedrons with the penultimate module Directions for making the compound of 5 tetrahedrons (pictured above) Directions for making greater/lesser stellated dodecahedrons with Jeannine Mosely's module Sketchy directions for making the compound of 12 dodecahdrons. (This assumes you're familiar with the penultimate module above).

Collection of practical polyhedra images by George W. Hart

Stellated Icosahedra There are 59 stellations of the icosahedron. These pages contain various images of these stellations and some background information. This information is an excerpt of an article published in Mathematica in Education . An expanded version appears in Chapter 10 of R. Maeder's book The Mathematica Programmer II. About the Stellated Icosahedra About the Images on These Pages ...

This Java 3d Viewer renders faceted and wireframe objects -- 20 included, AND it can fetch from a URL address -- all of the Platonic Solids and a variety of file formats ( .obj, .wrl, .nff, .off ), and it allows you to rotate them.

Polyhedra last updated 4 June 2002 Uniform Polyhedra: Displayed as solid and wire-frame models Johnson Solids: More solid and wire-frame models, plus some isomers to the Johnson Solids. Acrohedra: Polyhedra with a specified vertex, and tables of dihedral angles. Tessellations of the Plane: Uniform polygonal tessellations of the plane and NEW hyperbolic star tessellations. Locally Convex ...

Various resources about polyhedra and polytopes.

Mark Newbold's Java Applets ...

My newest work Shots of my Great Big Math Object Gallery 1 - 2 - 3 - 4 - 5 Gallery of work for sale Solids Jigs Math References Home - Drawings - Prints - Murals - Consumption - Stuff - Other Copyright 2002, Tom J. Lechner, lechner@inetarena.com ...

Java Applet: Stereoscopic Cross-Sections of 4-dimensional Star Polytopes ...

Work of Rev. Magnus Wenninger, monk of Saint John's Abbey, mathmathics and polyhedra ...

PPL Home Documentation Download Applications Credits Mailing Lists Bugs Links About PPL: The Parma Polyhedra Library What Is the PPL The Parma Polyhedra Library (PPL) is a modern C++ library for the manipulation of convex polyhedra. To be more precise, the PPL can handle all the convex polyhedra that can be defined as the intersection of a finite number of (open or closed) hyperspaces, each ...

This is a content based Educational website. Our goal is to deliver Geometric modeling plans and procedures to students and teachers via the Internet. Discover mathematics in a new way, through your hands and eyes.

Martin's Pretty Polyhedra What are they Fair question - I can't answer it - but I can tell you how I produced them and hundreds like them. Some have similarities to the domes designed by the architect Buckminster-Fuller (and the C60 molecule named after him, Buckminsterfullerene) and to other geodesic structures. One day while just sitting and thinking a question came into my mind. What would ...

Peek N-dimensional polytope visualization by cross-section and projection Peek is a program to interactively explore arbitrary dimension polytopes through the use of cross-sections and projections. Projections have already been extensively used for this purpose. For instance, those who know what a hypercube is have probably seen the projective views that are so common, such as the two shown here.

ABOUT: POINTERS: 52B: Polytopes and polyhedra Introduction Here are a few files concerning geometric objects made from straight pieces: polygons, polyhedra, and generalizations. History Applications and related fields Questions regarding the underlying spaces (and algebraic invariants) are included on the topology pages. Classic questions regarding polygons and regular solids are included on the ...

Java Applet: HyperSpace Polytope Slicer ...

Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah The Platonic Solids A platonic solid is a polyhedron all of whose faces are congruent regular polygons, and where the same number of faces meet at every vertex. The best know example is a cube (or hexahedron ) whose faces are six congruent squares. Manipulating the shapes on this page. If you have a Java ...

The book on polyhedra - geometry, mathematics, history.

Polyhedra Home The Uniform Polyhedra and Duals Polyhedra Gallery Polyhedra 2001 Credit to Zvi Har'El and Roman E Mader as it's their programs that generate the basic data for the uniform polyhedra. I'll take the credit for eveything else :). Thanks to the POV-Ray team for making a great ray tracer, which is free! View in full screen at 1024x768 or larger for best results! Images Sam Gratrix ...

Objects that cannot be taken apart with two hands Have you ever felt, when you were trying to put something together, that you needed an extra hand This sculpture represents research results on the number of hands that a robot would need to assemble collections of simple geometric objects. It is made from 30 identical aluminum tubes, grouped and colored as five twisted tetrahedra. The ...

Models, photographs and stereo image pairs of infinite regular polyhedra. VRML models can be interactivily tiled in 3 dimensions.

Circumnavigating a cube and a tetrahedron by visiting all of the sides or all of the edges Henry Bottomley September 2001 This page is related to a page on Surface distances on a cube or cuboid Consider the following set of problems for a polyhedron: 1a. What is the shortest possible closed route on the surface of the polyhedron which crosses each face once 1b. What is the shortest possible ...

Main Page Snapshots Animations Download Manual Feedback Disclaimer & Licence Polyhedra Home Email Me Polyhedra 2001 Main Page Polyhedra 2001 is an OpenGL program which displays the Uniform Polyhedra and related shapes in real time. The Uniform Polyhedra may be morphed in to their dual, exploded, truncated and unfolded into a net. There are other neat things too, even a polyhedra solar system!

The Fifth Platonic Solid - face-connected dodecahedral constructions ...

George Olshevsky's polychora George W Hart's Pavillion of polyhedra Fr. Magnus Wenninger's home page Roman Mader's polyhedra S. Dutch's crystlas & polyhedra V. Bulatov's polyhedra collection This homepage is constructed and maintained by Rolf Asmund. Please mail me at ra@kampsax.dtu.dk for comments and suggestions D. Eppstein's Geometry Junkyard Gordon's peek into the 4th dimension All the fair ...

The Many Faces of Polyhedrons Back to Tom York's page. Left to right: A truncated icosahedron, a small rhomibcuboctahedron, and a snub dodecahedron as seen in The Many Faces of Polyhedrons. This is a program that I (Tom York) wrote which allows you to interactively manipulate virtual regular polyhedrons (cube, dodecahedron, etc.) and semiregular polyhedrons (e.g. the truncated icosahedron the ...

Polyhedra At this gallery of polyhedra, all of which can be made from books in the Tarquin catalogue, not only can you view some amazing polyhedral models but you can also view and manipulate them in three dimensions - virtual reality! To do this you will need the appropriate 3D Plug-in for your browser. If you are using Netscape, you can download Netscape's Live3D VRML add-on. If you are using ...

Collecion of Polyhedra, with virtual reality models.