# polyhedra

share## Examples

polyhedra's examples

- You can print out the nets from Paper Models of Polyhedra. ( It is best to use nets witht flaps. And it is an interesting question to figure out how many flaps you need.) One of the purposes of this page is to discuss the relative merits of the different plastic kits. —
*“Polyhedra”*, math.nus.edu.sg - Archimedes of Syracuse knew that there exist 13 convex semiregular polyhedra. Archimedes considered the problem how many
**polyhedra**can be obtained if we use 2 or more combinations of regular polygons. —*“Archimedean Polyhedra;”*, - Regular
**polyhedra**generalize the notion of a regular polygon to three dimensions. Let n denote the number of faces of the polyhedron. Let s be the length of an edge, Sn. —*“Regular Polyhedra”*, tgers.edu - . an interactive collection of 3-d models. 3-d models on this site use Javascript; unfortunately your web browser does not have Javascript enabled. It's most likely that your browser supports it but that you have it turned off: please turn it on. —
*“: interactive models based on the canvas element”*, - Encyclopedia of Polyhedra, with virtual reality models.
**Polyhedra**have an enormous aesthetic appeal and the subject is fun and easy to learn on one's own. —*“Virtual Reality Polyhedra”*, - Free paper models: Platonic solids, Archimedean solids and many other
**polyhedra****Polyhedra**are beautiful 3-D geometrical figures that have fascinated philosophers, mathematicians and artists for millennia. —*“Paper Models of Polyhedra”*, - A polyhedron (plural
**polyhedra**or polyhedrons) is often defined as a geometric object with flat faces and straight edges (the word polyhedron comes from the Classical Greek πολυεδρον, from poly-, stem of πολυς, "many," + -edron, form of εδρον, "base", "seat", or "face". —*“Polyhedron”*, schools- - Naming, counting and measuring
**polyhedra**or polytopes. From obscure tetragonal antiwedges (chiral hexahedra) to popular buckyballs. —*“Polyhedron, Polyhedra, Polytopes - Numericana”*, - Collection of discussions regarding volume, vertices, dissection, g-holed tori, and other subjects. Here are a few files concerning geometric objects made from straight pieces: polygons, polyhedra, and generalizations. —
*“52B: Polytopes and polyhedra”*, math.niu.edu - A polyhedron is a solid figure in which each side is a flat surface. Regular Polyhedra. The cube and the tetrahedron are examples of Regular Polyhedra, also called Platonic Solids. A polyhedron is called regular if the. —
*“Polyhedra”*, - A polyhedron (plural
**polyhedra**or polyhedrons) is a geometric solid in three dimensions with flat faces and straight edges. Grünbaum (1994, p. 43) observed, "The Original Sin in the theory of**polyhedra**goes back to Euclid, and through Kepler, Poinsot, Cauchy and many others [ in that] at. —*“Polyhedron - Wikipedia, the free encyclopedia”*, - Description of the Forms Belonging to the 235 and m35 Icosahedral Point Groups Starting from the Pairs of Dual Polyhedra: Icosahedron-Dodecahedron and Archimedean Polyhedra-Catalan Polyhedra. Composite form. with icosahedral symmetry. resulting from the intersection. —
*“Icosahedral Polyhedra”*, mi.sanu.ac.rs - If you count the number of faces (the flat surfaces), vertices (corner points), and edges of a polyhedron, you can discover an interesting thing: The number of faces plus the number of vertices minus the number of edges equals 2. This can be written neatly as a little equation: F + V - E = 2. —
*“Polyhedron”*, **Polyhedra**have fascinated mathematicians for centuries, and this course will at least These days,**polyhedra**and polygonal meshes are ubiquitous in computer graphics, computer. —*“Algorithms for Polyhedra”*, cs.uwaterloo.ca- English: A polyhedron is a geometric shape which in mathematics is defined by three related meanings. Further generalizing the latter, there are topological polyhedra. —
*“Category:Polyhedra - Wikimedia Commons”*, - Real polytopes are a consistent mathematical formulation of the true geometric figures that we instinctively think of as "polygons", "polyhedra" and so on, in contrast to such things as abstract polytopes on the one hand and the woolly ideas. —
*“Polyhedra Index Page”*, - The total lack of a single book dealing, in a succinct manner, with the origin, development and natural geometric construction of the most important duals of the thir*** semiregular Archimedean
**polyhedra**was the inspiration for this unique work. —*“Polyhedra - Poliedri - Homage to/Omaggio ad Ugo Adriano Graziotti”*, - A polyhedron (plural
**polyhedra**or polyhedrons) is a geometric object with flat faces and straight edges.**Polyhedra**have fascinated mankind since prehistory, were first studied formally by the ancient Greeks, and continue to fascinate students, mathematicians and artists today. —*“”*, - Encyclopedia article about polyhedra. Information about
**polyhedra**in the Columbia Encyclopedia, Computer Desktop Encyclopedia, computing dictionary. regular polyhedra. —*“polyhedra definition of*, encyclopedia2**polyhedra**in the Free Online Encyclopedia” - Platonic and Archimedian Polyhedra. The five Platonic regular
**polyhedra**and the 13 semiregular polyhedra. Warning: Some netscape versions may not exponentiate properly: i.e. It would not be clear that x2 means x squared The Archimedean, or semi-regular polyhedra, are 'facially' regular. —*“Polyhedra”*, faculty.fairfield.edu - Includes pointers on geometric properties of polygons, polyhedra, and higher dimensional polytopes. —
*“The Geometry Junkyard:*, ics.uci.edu**Polyhedra**and Polytopes” - Cubes, prisms, and pyramids are examples of polyhedra. A polyhedron surrounds a bounded volume in three-dimensional space; sometimes this interior volume is considered to be part of the polyhedron, sometimes only the surface is considered, and occasionally only the skeleton of edges. —
*“Polyhedron - New World Encyclopedia”*,

## Videos

related videos for polyhedra

**The uni-stable polyhedron ()**Prof. John Conway proved that there are uni-stable polyhedra. That is to say, polyhedra which are stable on only one face. More information is available from**3D GEOMETRIC MODULAR POLYHEDRA ORIGAMI**12 POINTED POLYHEDRON BLUE AND YELLOW COLORS. THIS TAKES 12 SHEETS OF SQUARE PAPER TO CONSTRUCT.**Interactive Continuous Collision Detection for Non-Convex Polyhedra**We present a highly interactive, continuous collision detection algorithm for rigid, general polyhedra. Given initial and final configurations of a moving polyhedral model, our algorithm creates a continuous motion with constant translational and angular velocities, interpolating the initial and final configurations of the model. Then, our algorithm reports whether the model under the interpolated motion collides with other rigid polyhedral models in environments, and if it does, the algorithm reports its first time of contact (TOC) with the environment as well as its associated contact features at TOC. Our algorithm is a generalization of conservative advancement to general polyhedra. In this approach, we calculate the motion bound of a moving polyhedral model and estimate the TOC based on this bound, and advance the model by the current TOC estimate. We iterate this process until the inter-distance between the moving model and the other objects in the environments becomes below a user defined distance threshold. We pose the problem of calculating the motion bound as a linear programming and provide an efficient, novel solution based on the simplex method. Moreover, we also provide a hierarchical advancement technique based on bounding volume traversal tree to generalize the conservative advancement for non-convex models. Our algorithm is relatively simple to implement and has very small computational overhead of merely performing discrete collision detection multiple ...**Two Polyhedra with D2 Symmetry**The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. This Demonstration shows two polyhedra with D2 symmetry type, namely the rhombic dodecahedron of the second kind and the bilunabirotunda. Contributed by: Izidor Hafner**Polyhedra with Harp, Dog and Sea**Here is my latest stop-motion animation. It features several polyhedra that I made from paper and glue. The music is original, composed by me. I sequenced the voices and things on the computer, and played the harp myself. It's a little 22-string Celtic harp, tuned to Dm Dorian.**Polyhedra orbiting planetary mobile type thing**A mobile I made using nets downladed free from , some fishing line and clear perspex tube. Music track is Air by Beyond Absence**E8 POLYHEDRA UNIFIED FIELD THEORY**E8 POLYHEDRA UNIFIED FIELD THEORY AS I SEE IT**Space-Filling Polyhedra**The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. This illustrates four of the various polyhedra that can fill space. Drag the graphic to see the resulting polyhedra from different vantage points. By Ed Pegg Jr**Transparent equilateral polyhedron with 60 heptagons**The polyhedron consists of 12 regular pentagons, 60 equilateral triangles and 60 equilateral heptagons, that look almost regular. All the pentagons ly completely inside the polyhedron and therefore the model was built with transparent heptagons. Pictures can be found at At sourceforge a share a progrom that shows similar polyhedra: You can deform this polyhedron into a Great Icosahedron as follows: Extend the heptagons such that the triangles and the pentagons inside dissappear. The heptagons are kites now. The kites can be grouped into 12 times 5 kites that almost lie in one plane. You can twist the kites around that pair of vertices that were formed above the old triangles. Twist them such that every group of 5 kites lie exactly in one plane. What is left is a Great Icosahedron.**Origami Sonobe Series part 2 how to make a triangle polyhedra**A tutorial on how to make an origami triangle polyhedra. my channels are and thanks for watching please subscribe :)**AlgTop8e: Polyhedra and Euler's formula (last)**We investigate the five Platonic solids: tetrahedron, cube, octohedron, icosahedron and dodecahedron. Euler's formula relates the number of vertices, edges and faces. We give a proof using a triangulation argument and flow down a sphere. This is the fifth and final video of the eighth lecture in this beginner's course on Algebraic Topology, given by Assoc Prof NJ Wildberger of the School of Mathematics and Statistics at UNSW.**Dual polyhedra****Making more polyhedra (step 2)**This is the second part for making a cuboctahedron out of hanger tape and cable ties**Cross Sections of Regular Polyhedra**The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. Three noncollinear points determine a plane. Fix three points on the edges of a polyhedron and visualize the corresponding cross section. For a cube, the resulting polygon can be a triangle, a quadrilateral, a pentagon, or a hexagon. Contributed by: Oleksandr Pavlyk and Maxim Rytin**origami polyhedron (sonobe)**this is my 2nd video of making origami tutorials so i have bad quality in my videos but i dont have better digital camera! so dont say nothing about quality! and SUBSCRIBE**Marvin Solit on Hierarchy of Polyvertexia (Polyhedra)**This clip is from the late Dr. Marvin Solit's workshop on "Hierarchy of Polyvertexia (Polyhedra)" at the Synergetics Collaborative's Third Annual Summer Workshop on "Structure" at John Belt's Design Studio, Department of Technology, SUNY Oswego (23 July 2005). This video assumes knowledge of some technical geometry vocabulary. Here is a partial glossary with links to Wikipedia: Vector Equilibrium is Bucky's name for the cuboctahedron: 30-verti is Marvin's name for the icosidodecahedron: The dodecahedron, icosahedron, cube and octahedron are "platonic solids": Rhombic triacontahedron: Rhombic dodecahedron: Enneacontahedron: Compound of five cubes: Isotropic vector matrix: Hoberman sphere: Dr. Marvin Solit was a founding member of the Synergetics Collaborative and The Foundation for New Directions (FND), a center for the exploration of holistic living in Cambridge, MA. 167MB QuickTIme The Synergetics Collaborative's Third Annual Summer Workshop "Structure" at John Belt's Design Studio brought together 33 people to work on and discuss Structure in its broadest sense especially as related to Bucky Fuller's Synergetics. A full report on the event with photos is available at The Synergetics Collaborative (SNEC) is a 501(c)(3) non-profit organizing events for ...**Making Polyhedra (step 2)**Using "building blocks" (from square pieces of paper and assembling polyhedra.**Polyhedra, Spheres, and Cylinders**The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. This Demonstration displays the Platonic solids, the Archimedean solids and their duals, and the Kepler-Poinsot polyhedra. You can make the faces disappear or change the radii of the spheres and cylinders used for the vertices and edges. Contributed by: Russell Towle**Nanodots - Dual Polyhedra**This is an example of the dual polydhedra of the Platonic solids. Inside the hexahedron (cube) frame is a octahedron (diamond). The octahedron itself is made from squares and triangles. Made with Nanodots - better than the neocube in my opinion. You construct the dual polyhedron by taking the vertices of the dual to be the centers of the faces of the original figure. The edges of the dual are formed by connecting the centers of adjacent faces in the original. In this way, the number of faces and vertices is interchanged, while the number of edges stays the same.**Chemistry 101 Part 4****AlgTop8: Polyhedra and Euler's formula**We investigate the five Platonic solids: tetrahedron, cube, octohedron, icosahedron and dodecahedron. Euler's formula relates the number of vertices, edges and faces. We give a proof using a triangulation argument and the flow down a sphere. This is the eighth lecture in this beginner's course on Algebraic Topology, given by Assoc Prof NJ Wildberger of the School of Mathematics and Statistics at UNSW.**Another Polyhedron with Equilateral Heptagons,**A added this video after a request in a comment on this video It is a polyhedron that consists of 60 equilateral heptagons, 30 rhombi and 20 regular pentagons.**Double Flippy Flippy Faced Polyhedra**Folded from a single equalateral triangle**Michael Burt on the Polyhedral Universe at Noguchi Museum 2005**This clip is from Michael Burt's talk on "The Periodic Table of the Polyhedral Universe" from the Synergetics Collaborative's Fall 2005 Symposium on "Synergetics in the Arts" at the Noguchi Museum (19 Nov 2005). Burt discusses his effort to classify all of the various classes of polyhedra into one comprehensive "periodic table". 16 MB QuickTime: The Synergetics Collaborative's 2005 Symposium on "Synergetics in the Arts" at the Noguchi Museum brought together 77 people from around the world to discuss some of the work attendees have been doing related to the intersection of Buckminster Fuller's Synergetics and the arts. The Synergetics Collaborative (SNEC) is a 501(c)(3) non-profit organizing events for anyone with an interest in learning about or building upon Buckminster Fuller's Synergetics. Video producers: Victor Acevedo, Digital artist and Visual Music producer/director. A member of SNEC and a long-time student of RBF and Synergetics. Recently he's been working with Synergetics Collaborative member Thomas Miller on his Synergetics 3.0 project. Eric Acevedo has been working in video production for over 25 years. He was involved first in the entertainment industry and then more recently in documentary and educational video projects. In November 2005 he produced and directed the complete recording of the Synergetics Collaborative's symposium called "Synergetics in the Arts" at the Isamu Noguchi Museum.**polyhedron.wmv**an attempt at a flexible polyhedron. The first part of clip shows a half form and how the edges of the opening appear to remain on a plane during flex. second part shows a closed form built from two of these halves. no numeric ***ysis attempted. closer inspection revealed non-planar movement of the half form opening, suggesting that the closed form is not truly flexible. The bellows theorem would seem to disallow the apparent planar movemnent of the top edges of the half form. If this was possible, then joining two of the half forms with a square profile foldable tube would create a true bellows. Thanks to R. Connelly and R. Lang for their advice.**Making more polyhedra (step 1)**This is first step for making a cuboctahedron from hanger tape and cable ties.**Stella, Polyhedron Navigator: creating new compounds**How to create new polyhedral compounds by replacing each part with a new shape using Stella4D or Great Stella (www.software3**Zoetrope Polyhedra 1**Morphing polyhedron zoetrope. By Kevin Klinkel. Craft Technology Group, CU Boulder.**polyhedra XL iPad - Simulator Gameplay Promo**A quick video showing polyhedra XL for the iPad. It doesn't show off the (very cool) accelerometer integration, but it gives you an idea of what the game is. You're able to rotate the device and have all of your shapes fall towards the new bottom of the screen.**Magic Polyhedra Club**Magic Polyhedra Club at Diamond Bar High School Timothy Huang Henry Liu Caleb Lau Adeel Mohammadi**Polyhedra for iPad**Leanna takes a look at Polyhedra XL on iPad.**Making Polyhedra (step 1)**A square piece of paper will be folded to make a "building block" for polyhedra.**E8 POLYHEDRA UNIFIED FIELD THEORY MATHS ART**E8 POLYHEDRA UNIFIED FIELD THEORY MATHS ART SCIENCE GEOMETRY PHYSICS aviation space computer mechanics video game medicine gadget environment electronics diy nano Wayne Brydon**folding Flippy Faced Polyhedra - part 1**A two in one demonstration - Fold a 16 face 8 flip polyhedra then collaps this fold to make a Cube with 6 faces and flips**Unfolding Polyhedron Nets**The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. A polyhedron can be unfolded from a series of connected faces in 3D to form a net of faces in a single plane. Two of the simplest polyhedra, the cube and tetrahedron, are presented here for interactive unfolding. Contributed by: Jon McLoone**E8 POLYHEDRA-LEONARDO DAVINCI NEW SECRETS REVEALED CHECK IT OUT**I have compiled alot of my work with Davinci's to create a new lot of work.Please check it out you wont be disapointed.**Polyhedral Cubes**Students Sarah Cuveele, Charlotte De Baets and Glenn de Hondt made the movie to which I added a composition by Frank Michiels.**Generalized Waterman Polyhedra**The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. The Waterman polyhedra display the convex hull of the lattice points within radius sqrtr of a given center. This Demonstration offers three lattices (body-centered cubic, face-centered cubic, simple cubic) and a variety of possible centers, with the ... Contributed by: Ed Pegg Jr**polyhedra - iPhone & iPod Touch**YES, PHYSICS *CAN* BE FUN!!! Use gravity to your advantage in this addicting physics-based action game! The Goal Fill more than 66% of the screen with shapes to complete a level. The game ends when you run out of shapes. Sounds easy, right? Think again! There are enemy particles and other shapes to worry about! FEATURES - Real physics-based interaction; watch the different shapes hit and roll off each other based on real mass and gravity! - Use the accelerometer to change gravity...you can use this to your advantage - Unlimited levels...your only limitation is how well you do - 6 different Zones to play...each one offers unique challenges - Global online leaderboards...rank yourself amongst other players worldwide! 6 different leaderboards to rank your scores. (Global leaderboard functionality provided by the AGON Online Social Platform for iPhone Games.) - Play around in the Toy Box as long as you like...create and remove shapes, move them around, rotate the screen to watch them fall. Set the song you like and the background colors you like. The choice is yours! - Listen to the over 8 minutes of original music, or play the game listening to your own iPod music - Colorful and fluid graphics COMING SOON - Awards: receive awards as you play. Put them on your leaderboard wall to show all the other players how good you are!**5 minute demo of Polyhedra IMDB**A quick demo of Polyhedra IMDB, including starting up a fault-tolerant database service, querying and modifying the database via SQL, monitoring changes via 'active queries', performing a fail-over, and dynamically modifying the database structure without interrupting existing client applications.

## Blogs & Forum

blogs and forums about polyhedra

*“The interview went well, I think, and perhaps she will be calling me back for a second interview in a couple of days. admin's blog. Login or register to post comments. New Drupal Web site! Sun, 10/04/2009 - 15:34 — admin. A new Drupal Web site has been published:***Polyhedra**Drupal”*— Blogs |***Polyhedra**Drupal,*“Posts for Polyhedra”**—***Polyhedra**| Enea Blog, enea.web5*“Unistable***polyhedra**" Home : Blog : August 2005. Unistable polyhedra. Monday 29 August 2005. These days, Kellogg's cereals have Disney wobblers in them. Because of their round bottoms and a very low center of gravity, they wobble but end up standing upright”*— Ned Batchelder: Unistable polyhedra,**“The blog of the DigitalRune Team (Helmut Garstenauer, Martin Garstenauer) Blog. Forum. License FAQ. Online Documentation. Mathematics, collision detection and game physics libraries for .NET/XNA. Read more Blog. Fast Support Mapping for Convex Polyhedra. Sep 17”**— DigitalRune Blog - Fast Support Mapping for Convex Polyhedra,**“[Archive] Wild and Wacky***Polyhedra**Modeling Contest Contests 1. Your model MUST be made with a polyhedra, and only a polyhedra. 2. No more then 1000 polygons. 3. All models must be submitted by the end of September 30, 2010”*— Wild and Wacky***Polyhedra**Modeling Contest [Archive, cheetah3*“Twisted***Polyhedra**program was the previous entry in this blog. entry in this blog. Find recent content on the main index or look in the archives to find all content”*— Twisted***Polyhedra**version 1.1 - Puzzling Addiction,*“Description Video Reviews Twitter Forum.***polyhedra**XL. Add a New Topic Reply to Post. Be the first to discuss this app. Reply to © Simple:Press Forum. Last blog entries. 5 Apps to Help You Rise and Shine. Posted in Health & Fitness, Lifestyle, Utilities on Nov,”*— iPhone, iPod Touch, iPad Application List " Forum " Games,**“Polyhedra are beautiful 3-D geometrical figures that have fascinated philosophers, Polyhedra. Here are some very nice pictures of Decorated Polyhedra”**— \ Ursi's BLOG /, ursispaltenstein.ch*