polyhedra
DESCRIPTION
Polyhedra. STEM Cats 2014. Tessellations. M.C. Escher. Buckminsterfullerene. Common Cold Virus. Bogota Sport Center. Epcot. Dice. Seven Days Sci Fi TV Series. Rubies. Giant’s Causeway. Origami. Lamps. Projection of Cube. Projection of a Hypercube. Projection of a Hypercube. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/1.jpg)
Polyhedra
STEM Cats
![Page 2: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/2.jpg)
Tessellations
![Page 3: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/3.jpg)
![Page 4: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/4.jpg)
![Page 5: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/5.jpg)
![Page 6: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/6.jpg)
![Page 7: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/7.jpg)
![Page 8: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/8.jpg)
M.C. Escher
![Page 9: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/9.jpg)
Buckminsterfullerene
![Page 10: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/10.jpg)
Common Cold Virus
![Page 11: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/11.jpg)
Bogota Sport Center
![Page 12: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/12.jpg)
Epcot
![Page 13: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/13.jpg)
Dice
![Page 14: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/14.jpg)
Seven Days Sci Fi TV Series
![Page 15: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/15.jpg)
Rubies
![Page 16: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/16.jpg)
Giant’s Causeway
![Page 17: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/17.jpg)
Origami
![Page 18: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/18.jpg)
Lamps
![Page 19: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/19.jpg)
Projection of Cube
![Page 20: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/20.jpg)
Projection of a Hypercube
![Page 21: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/21.jpg)
Projection of a Hypercube
![Page 22: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/22.jpg)
Many Hypercubes
![Page 23: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/23.jpg)
Delete Half of the Edges to get
Diamond
![Page 24: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/24.jpg)
Challenge #1
Construct as many tessellations as you can with identical regular polygons
![Page 25: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/25.jpg)
Challenge #2
Construct as many tessellations as you can with the following properties
All tiles are regular polygons
There are at least two different kinds of tiles
The same sequence of tiles meets around each vertex
![Page 26: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/26.jpg)
Challenge #3
Construct as many polyhedra that you can with the following properties
All faces are equilateral triangles
All edges bend “outward”– the polyhedron is convex
![Page 27: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/27.jpg)
Challenge #4
Construct as many polyhedra that you can with the following properties
All faces are identical regular polygons
The same number of faces meet at each vertex (corner)
![Page 28: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/28.jpg)
Challenge #5
Construct as many polyhedra that you can with the following properties
All faces are regular polygons
There are at least two different kinds of faces
The same sequence of faces meets around each vertex
![Page 29: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/29.jpg)
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/
![Page 30: Polyhedra](https://reader035.vdocuments.us/reader035/viewer/2022062718/56812b68550346895d8f8a46/html5/thumbnails/30.jpg)
Image Sources http://www.georgehart.com/virtual-polyhedra/escher.html
http://it.wikipedia.org/wiki/Fullereni#mediaviewer/File:Fullerene-C60.png
http://www.lightnessofbeingbook.com/LOBColorPlates/images/Plate03b_IcosVirus.jpg
http://www.domusweb.it/en/architecture/2012/01/04/el-bosque-de-la-esperanza.html
http://images.frpgames.org/products/product_36488.jpg
http://i1.sell.com/u/3H/5G/5BQ/4706433-l.jpg
http://images.nationalgeographic.com/wpf/media-live/photos/000/011/cache/rubies_1176_990x742.jpg
http://shearings-cdn2.zolvtravel.com/DynamicImages/d510/d510755c6e739c2465038ddea2f849d0_640_480-634873692367638135.jpg
http://michal.kosmulski.org/origami/icosidodecahedron-jitterbug.jpg
http://media.tumblr.com/tumblr_lefroeVII61qeb9gf.jpg
http://www.jeffreyventrella.com/Old_Art/cuboctahedron_big.jpg
http://www.wdwinfo.com/Photos/600-spaceship-earth3.jpg
http://upload.wikimedia.org/wikipedia/commons/d/d9/Rhombic_dodecahedra.png