# 3D Geometry

Entering the 3rd dimension!

22 Lessons

## Facet Counting

#### Course description

Explore the fundamental concepts of three-dimensional geometry: What strangely-shaped 3D pieces can result from slicing up 3D polyhedra with planes? What flat polygons can fold up into 3D shapes? If you're running around on the surface of a cube-world, what's the shortest path between two opposite corners? (The answer to this last one might surprise you.)

In this course, you'll stretch problem-solving techniques from flat figures into a third-dimension and explore some mathematical ideas and techniques completely unique to 3D geometry. For example, you'll investigate and learn how to apply Euler's facet counting formula, a formula which describes a surprising algebraic relationship that relates the number of corners, edges, and faces that any polyhedron can have.

#### Topics covered

• Cross Sections
• Dissecting Shapes
• Distance in 3D
• Dual Polyhedra
• Euler's Formula
• Folding
• Nets
• Paths on a Surface
• Platonic Solids
• Polyhedra