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Posted on 23rd Jul at 12:53 AM, with 76 notes

spring-of-mathematics:

Polytopes in Geometry.

In elementary geometry, a polytope is a geometric object with flat sides, which exists in any general number of dimensions. A polygon is a polytope in two dimensions, a polyhedron in three dimensions, and so on in higher dimensions (such as a polychoron in four dimensions). Some theories further generalize the idea to include such objects as unbounded polytopes (apeirotopes and tessellations), and abstract polytopes. When referring to an n-dimensional generalization, the term n-polytope is used. For example, a polygon is a 2-polytope, a polyhedron is a 3-polytope, and a polychoron is a 4-polytope…See more : History and Different approaches to definition at Polytope on Wikipedia.
In  “Universal constructors in polytopal graph theory”, a article about Polytopal graph theory, the author wrote:
Polytopal graph theory is concerned with the graphs formed by the edges and vertices of polytopes. The graph of a simple polytope contains all of the necessary information to recover its full combinatorial structure in polynomial time, and thus is equivalent in a strong sense to the object. These objects are both mathematically and aesthetically beautiful as well as practically relevant.  Properties of polytopal graphs are linked with a number of important algorithmic questions about polytopes such as the complexity of  linear programming and the convergence of randomized algorithms - Source.

Image: Polytope movie page (Hypercubes) by Komei Fukuda - A Catalog of Uniform Polytopes by Jenn - Polytope on Wikipedia&  Cubic Soap by Jeff Buchbinder.
 
Posted on 22nd Jul at 3:23 PM, with 337 notes
0rgazmus:

Mostanában nemcsak a heti egy gyros tálra van igényem, de sajnos a Zing valamelyik burgerére is. Rákattantam.
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0rgazmus:

Mostanában nemcsak a heti egy gyros tálra van igényem, de sajnos a Zing valamelyik burgerére is. Rákattantam.

Posted on 22nd Jul at 12:23 PM, with 5,782 notes
dontkillseanbean:

Brace yourselves, Legends is coming. And so our death watch begins… 
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dontkillseanbean:

Brace yourselves, Legends is coming. And so our death watch begins… 

Posted on 22nd Jul at 2:55 AM, with 23 notes
90377:

i photographed something creepy sitting in a bush
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90377:

i photographed something creepy sitting in a bush

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