This artifact is from an activity we did (my table partner and myself) during Week Four to help us better understand space figures and polyhedra. The activity had us cut out and fold paper in a way that made the figures pictured to the left, also known as the five platonic solids, the tetrahedron, cube, octahedron, dodecahedron, and the icosahedron. 

What is a Polyhedron?

A polyhedron is described as, "a three-dimensional figure with flat polygonal faces, straight edges, and vertices." A visual example are the figures pictured in the top left. The faces are the flat sides of the polyhedron, they are two-dimensional polygons. The edges are the line segments formed where two faces meet. The vertices are the point of intersection of at least two edges. 

Similar to polygons, there are two types of polyhedrons, concave and convex. Convex polyhedrons are described as being able to have, "a line segment join any two points on the surface of a polyhedron lies completely within the polyhedron." In other words, there are no dents, dips, etc. Whereas, concave polyhedrons are the opposite, they do have dents, dips, valleys, etc. and you could not connect a line segment that stays completely within the polyhedron. 

Polyhedra also use the same "code" to communicate designs, you pick a vertice and count the number of sides the regular polygons around it has. An example of a polyhedron code for a semi-regular polyhedron made up of hexagons and pentagons would be 6, 6, 5 or hexagon, hexagon, pentagon. 

In order to find the number of faces (F), vertices (V) and/or edges (E) of any polyhedron we have to use Euler's Formula. Euler's Formula states that          F + V - E = 2. This formula can be used to help determine the existence of a polyhedron, as well as solve for an unknown number of faces, vertices or edges (as long as you have at least two of the other quantities). 

What are the Five Platonic Solids?

The five platonic solids are also known as the "regular" polyhedra, due to their faces being made up of one congruent regular polygon. All five of these polyhedrons are shown in the picture above. The tetrahedron is the yellow figure made up of four triangular faces, the cube is the light blue figure made up of six square faces, the octahedron is the orange figure made up of eight triangular faces, the dodecahedron is the slightly darker blue/turquoise figure with twelve pentagonal faces, and the icosahedron is the red figure made up of 20 triangular faces. 

Similar to semi-regular tessellations, polyhedra made up of faces of two or more regular polygons are considered semi-regular polyhedra. 

 My Understanding of Polyhedrons

Up until this point in class I had remembered briefly talking about polyhedra in elementary school, although I can't remember exactly when. I did already know what prisms, pyramids, cylinders, and cones were, however I didn't know the five platonic solids. I had also never remembered seeing Euler's Formula before, and that has proved to be extremely helpful when finding missing parts of polyhedrons or testing their validity. Overall, I don't feel like I was ever very confused or lost when it came to polyhedrons, I feel like everything we went over clicked pretty easily. I didn't have much prior knowledge besides the basics, so a lot of what we went over was new information for me.