Platonic Solids

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Platonic Geometry

Platonic solid is one unique type of the polyhedron solids which follow the rules of the Euclidean geometries. Platonic solid is a 3-Dimensional geometry, a polyhedron with the same polygons in its all faces. to explain what is a polyhedron, we can describe it as a geometry with flat faces, sharp angles and straight edges. There are  5 types of Geometries under this title; the Tetrahedron, the Hexa-Hedron, the Octa-hedron, the Dodeca-hedron and finally the Icosa-hedron.

 Tetrahedron:

Its a shape consists of 4-sides of triangles, or we can call it 3 sides pyramid

Hexa-Hedron:

Its a shape consists of 6-sides of squares , or simply, a cube

Octa-hedron:

Its a shape consists of 8-sides of triangles , or to describe it better, a mirrored 4-sides pyramid

Dodeca-hedron:

Its a shape consists of 12-sides of 5-sided polygon

Icosa-hedron:

Its a complex geometry consist of 20-sides of triangles

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On this Experiment, I tried to build a Dodecahedron, the one with 12 sides of five-sided polygons, actually it was not easy as it look like to be, the whole process require understanding of the mathematics of geometry, and its very hard to imagine.

Dodecahedron creation process start with a sphere, divided into two hemisphere, each 5 sided, but the upper one is shifted by 1/10, that was done by divide the circle into 10 points, and then take each second one, using the Module technique(the remaining of division %). the rest of the process was a sequence of connecting points between different levels of horizontal sections of the sphere.

The final part, was using the technique of evolutionary search to optimize the size of all sides. so each polygon in the shape have the same size.

 

Reference

http://www.designcoding.net/construction-of-icosahedron/

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

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

Visual Note:

if you look to the isometric of all of them, you will see the triangle

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