The Many Sides of the “Omnipoliedro”

    The Omni-polyhedron may seem new to many Americans, but Spanish students build these models. Originally called the “Omnipoliedro”, the shape is many polyhedrons, one hiding inside of another; an Icosahedron that fits around a Dodecahedron, which fits around a Hexahedron, or Cube, which goes over a Tetrahedron (a four-sided pyramid), and finally fits around an Octahedron. Often the edges of each polyhedron are colored, each polyhedron differently so that it is easier to define between them all. 

Our mission is to make one of these, but how?

The First Steps

Before we began creating the real deal, we used tape and straws to create a miniscule version of this structure, so that we can find any issues and blocks immediately. While we were making them we realized that some of the given equations had big errors, and that we needed to refine some of the operations.

Shapes and Patterns

The root to solving the exact lengths revolved on proportionalism; the length of one shape would always have something in common with another. For example, the length of the tetrahedron edge was congruent to the hypotenuse of a hexahedron face. However, one problem would be finding how to connect the pipes together, and adding those to the equation.

Creating the Life-sized Object

Our model is made out of PVC pipes, with zip ties to bind the pipes together and we used the given equations to find the lengths of each polyhedrons’ edge, and we’ve rounded each to a tenth of a centimeter for precision.

The Eye Bolts and Caps to Our Advantage

When we were measuring how long each side for each shape had to be, we realized that the eye bolts and caps would be a problem. The two combined added an extra six centimeters total to a whole edge, so when calculating the edges we subtracted the extra six centimeters. In the end, we resulted with this:

Polyhedron	Number of Lines	Length (cm)	Total Length Needed (cm)
Tetrahedron	6	135.4	812.4
Hexahedron (Cube)	12	94	1128
Octahedron	12	64.7	776.4
Dodecahedron	30	55.8	1674
Icosahedron	30	94	2820
Total needed for construction	24	304	7296

Putting The Pieces Together

    After cutting pipes, attaching caps, and spray painting, we were ready to assemble the Omnipoliedro. Dubbed as “The Shape,” the next days were spent preparing the pipes, drilling caps, tightening eye bolts, and painting each pipe. The problem with preparing each pipe was that once we were done, there was only one day to assemble the shape altogether.

Assembling The Real Deal

    We had to strategize which shapes would be created first, or else we’ll be building shapes before others, and they won’t fit in each other. The first shape assembled was the Octahedron, because it was the smallest one in the sequence: