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This one is a bit long: it is constructed starting with no less than

The overall symmetry of the 'animal' is

**92 regular dodecahedra**glued face-to-face between themselves: 12 of those are in**blue**, 20 further in**red**and the remaining 60 in**orange**. Pay attention now: the centers of the**blue (12)**and**red (20)**dodecahedra are the**32 vertices**of a**rhombic triacontahedron**(a**Catalan solid**dual to the**Archimedean icosidodecahedron**), the side of the rhombic triacontahedron is 4 times the radius of the sphere inscribed in a regular dodecahedron, that is sqrt(10 + 22/sqrt(5)). In all, the**complex**you are seeing is itself a great polyhedron of face vector [V= 1240, F= 864, E= 2160; genus: g= 29] (one hole per face of the said**rhombic triacontahedron**, that is 30 in all).The overall symmetry of the 'animal' is

**Ih**, that is,**icosahedral complete w. horiz. reflection**, the same of the regular dodecahedron & icosahedron. Post has shared content

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**Atom Builder**

Assemble your own atoms from buckets of Protons, Neutrons and Electrons and see where they are on the periodic table, their charge and atomic mass.

*Fun, interactive, research-based simulations of physical phenomena from the PhET™ project at the University of Colorado.*

**Here (expects HTML5):**http://goo.gl/RykXMV

More Science simulations (HTML5): http://goo.gl/MQKpAk

Older sims (inc. non HTML5): http://phet.colorado.edu/

PhET @ Wikipedia: http://goo.gl/Pyw4Bm

Podcast on Teaching with Interactive Simulations, featuring Katherine Perkins, Director of Physics Education Technology (PhET): http://goo.gl/aNF5hA

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The

The Penrose triangle was actually first created by the Swedish artist Oscar Reutersvärd in 1934. The mathematician Roger Penrose independently devised it in the 1950s, describing it as "impossibility in its purest form".

However, you can actually build a 3-dimensional object that looks like a Penrose triangle from the right perspective. You can see how that works here. But it's even more fun in real life!

For example: Brian MacKay & Ahmad Abas put a sculpture called

http://en.wikipedia.org/wiki/File:Perth_Impossible_Triangle.jpg

Penrose actually wrote about the Penrose triangle with his father, the psychiatrist Lionel Penrose, in a short article in the

This article also included a related impossible object, the

http://en.wikipedia.org/wiki/Waterfall_%28M._C._Escher%29

Both the Penrose triangle and Penrose stairs make sense 'locally' but not 'globally': if you look at a small region they look okay, but if you follow them around a loop you don't get back where you should. So, mathematically we say they are examples of 'cocycles' that aren't 'coboundaries'. Perhaps it's no coincidence that Penrose is an expert on cocycles and their role in physics - that's one of the ideas behind a theory he invented, called twistor theory.

For more impossible objects, see:

http://en.wikipedia.org/wiki/Impossible_object

Thanks to W Aden for pointing out the image here.

#illusions

**Penrose triangle**is often called an**impossible object.**But that depends on your perspective!The Penrose triangle was actually first created by the Swedish artist Oscar Reutersvärd in 1934. The mathematician Roger Penrose independently devised it in the 1950s, describing it as "impossibility in its purest form".

However, you can actually build a 3-dimensional object that looks like a Penrose triangle from the right perspective. You can see how that works here. But it's even more fun in real life!

For example: Brian MacKay & Ahmad Abas put a sculpture called

*Impossible Triangle*in the Claisebrook Roundabout in East Perth, in Australia. Seen from the right angle, it looks like a Penrose triangle! Check it out:http://en.wikipedia.org/wiki/File:Perth_Impossible_Triangle.jpg

Penrose actually wrote about the Penrose triangle with his father, the psychiatrist Lionel Penrose, in a short article in the

*British Journal of Psychology*called "Impossible Objects: A Special Type of Visual Illusion".This article also included a related impossible object, the

**Penrose stairs.**Both these were later used by the artist M. C. Escher. If you don't know what I mean, look at Escher's famous lithograph,*Waterfall*:http://en.wikipedia.org/wiki/Waterfall_%28M._C._Escher%29

Both the Penrose triangle and Penrose stairs make sense 'locally' but not 'globally': if you look at a small region they look okay, but if you follow them around a loop you don't get back where you should. So, mathematically we say they are examples of 'cocycles' that aren't 'coboundaries'. Perhaps it's no coincidence that Penrose is an expert on cocycles and their role in physics - that's one of the ideas behind a theory he invented, called twistor theory.

For more impossible objects, see:

http://en.wikipedia.org/wiki/Impossible_object

Thanks to W Aden for pointing out the image here.

#illusions

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