The Tetrahedron

In geometry, how many faces does a tetrahedron have?

And the answer: four.    

The prefix "tetra" means four. In geometry, a tetrahedron is a 3D shape that has four faces, like a pyramid.

Photo credit: public domain. 

While a tetrahedron might seem simple enough, it has many unique qualities much like that of the other platonic solids. Each face of a tetrahedron offers an equilateral triangle, and beautifully, all four vertices are the same distance from each other. Tetrahedrons are also the only platonic solid with no parallel faces.

You might also recognize this shape from games like Dungeons & Dragons — its perfectly even sides and angles make for fair dice. This designation is only granted to shapes which have an equal chance of landing on any face, and the tetrahedron's four equal faces make that pretty darn easy.

The tetrahedron is actually the only polyhedron that has four faces. It is also the only simple polyhedron that has no polyhedron diagonals (as in, no face diagonals or space diagonals). Interestingly, a regular tetrahedron can be formed using six of the face diagonals of a cube. The vertices of the tetrahedron coincide with four of the cube's vertices, making it fit snugly with very little effort. See for yourself:

Photo credit:

Learn more about the uses and importance of the tetrahedron below.

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