MC Escher Buckminsterfullerene Common Cold Virus Bogota Sport Center Epcot Dice Seven Days Sci Fi TV Series Rubies Giants Causeway Origami Lamps Projection of Cube Projection of a Hypercube ID: 1019466
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1. PolyhedraSTEM Cats
2. Tessellations
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8. M.C. Escher
9. Buckminsterfullerene
10. Common Cold Virus
11. Bogota Sport Center
12. Epcot
13. Dice
14. Seven Days Sci Fi TV Series
15. Rubies
16. Giant’s Causeway
17. Origami
18. Lamps
19. Projection of Cube
20. Projection of a Hypercube
21. Projection of a Hypercube
22. Many Hypercubes
23. Delete Half of the Edges to get Diamond
24. Combinatorial OptimizationThere are 100 people and 100 jobs. For each person and each job you know how much it will cost to (re)train that person to do that job. What is the least expensive matching of people to jobs?The number of possible matchings is 100! (100 factorial). There is not enough time left in the life of the universe to run through this list to check the cost of each matching.By understanding the properties of a certain polyhedron of dimension 10,000-199 (picture omitted!), this problem can be solved routinely in a fraction of a second.
25. Modeling, Visualization, and Math ArtPolyhedra are basic building blocks for 2- and 3-d modeling.Example of assembling a polyhedral puzzle, created with POV-Ray during my Visualizing Math course: http://www.ms.uky.edu/~lee/visualfa15/puzzle5.mov
26. Challenge #1 Construct as many tessellations as you can with identical regular polygons
27. Challenge #2 Construct as many tessellations as you can with the following propertiesAll tiles are regular polygonsThere are at least two different kinds of tilesThe same sequence of tiles meets around each vertex
28. Challenge #3 Construct as many polyhedra that you can with the following propertiesAll faces are equilateral trianglesAll edges bend “outward”– the polyhedron is convex
29. Challenge #4 Construct as many polyhedra that you can with the following propertiesAll faces are identical regular polygonsThe same number of faces meet at each vertex (corner)
30. Challenge #5 Construct as many polyhedra that you can with the following propertiesAll faces are regular polygonsThere are at least two different kinds of facesThe same sequence of faces meets around each vertex
31. Challenge #6 Find all flat shapes formed by six squares that can be folded up to make a cube. See also http://erikdemaine.org/metamorphosis/
32. Image Sourceshttp://www.georgehart.com/virtual-polyhedra/escher.htmlhttp://it.wikipedia.org/wiki/Fullereni#mediaviewer/File:Fullerene-C60.pnghttp://www.lightnessofbeingbook.com/LOBColorPlates/images/Plate03b_IcosVirus.jpghttp://www.domusweb.it/en/architecture/2012/01/04/el-bosque-de-la-esperanza.htmlhttp://images.frpgames.org/products/product_36488.jpghttp://i1.sell.com/u/3H/5G/5BQ/4706433-l.jpghttp://images.nationalgeographic.com/wpf/media-live/photos/000/011/cache/rubies_1176_990x742.jpghttp://shearings-cdn2.zolvtravel.com/DynamicImages/d510/d510755c6e739c2465038ddea2f849d0_640_480-634873692367638135.jpghttp://michal.kosmulski.org/origami/icosidodecahedron-jitterbug.jpghttp://media.tumblr.com/tumblr_lefroeVII61qeb9gf.jpghttp://www.jeffreyventrella.com/Old_Art/cuboctahedron_big.jpghttp://www.wdwinfo.com/Photos/600-spaceship-earth3.jpghttp://upload.wikimedia.org/wikipedia/commons/d/d9/Rhombic_dodecahedra.png