Workshop 1. PoCo Introduction

A Polyhedral Computing Experience

The space is unfolding in front of your eyes: a 3D simulation that will change the way you observe the real world. You manipulate 3D complex structures with unseen versatility. You experience pure communications with the space itself. You see a triangle, it is a triangle. No confusions, no gimmicks.

1. Hello PoCo!

PoCo is a computer program that allows you to play with polyhedra. Do you remember playing with cubes when you were a kid?

2. PoCo Playground

Now you can play with many and more complex objects: polyhedra and ensembles of polyhedra. Here you have the basic constituents of PoCo’s playground.

On the first row, notice the Platonic solids. Implied by the number of faces (4,6,8,12,20), their names are tetrahedron, cube (or hexahedron), octahedron, dodecahedron and icosahedron. On the second row, you see truncated versions of three of the Platonic solids (matching to the ones on the top row). They are Archimedean solids, obtained by truncation, or cutting corners, of the corresponding Platonic solids. They have in common something special: all faces are regular hexagons, of the same size. That will allow future interactions and the generation of large colonies of such polyhedra. Once you have a few operations available, you can create geometric expressions, by applying a series of operations. Such a geometric expression is illustrated below.

Bees are wonderful mathematicians. They realized that the most efficient structure to be used for constructing rooms with least material is the hexagonal structure. Humans were able to scientifically acknowledge that just recently.

Operations are key components to evolution: from elementary objects (cells, individuals) to colonies (communities). Working together as a group, ants, bees and humans are the best examples.

PoCo allows you to perform operations and transformations on geometric objects. To better understand the structure of the complex colonies of geometric objects, PoCo can show you the third dimension using movement. You can move, rotate and transform objects to understand their geometry.