AI Tutor
Every object you can hold—from a cereal box to a basketball—occupies three dimensions: length, width, and height.
In geometry, we classify these 3D objects into two main families: polyhedra, which have only flat surfaces, and curved solids.

Anatomy of Polyhedra

A polyhedron is a solid bounded entirely by flat polygon surfaces called faces.
The line segment where two faces meet is an edge, and the sharp corner point where three or more edges intersect is a vertex (plural: vertices).
How do we distinguish between flat-faced solids that have two identical ends versus those that taper to a single point?

Prisms vs. Pyramids

A prism has two congruent, parallel polygons called bases, connected by lateral faces that are parallelograms (or rectangles).
A pyramid has only one polygonal base, and its triangular lateral faces meet at a single shared point called the apex.
In 1752, Swiss mathematician Leonhard Euler discovered a universal relationship connecting the vertices (VV), edges (EE), and faces (FF) of any convex polyhedron: Euler's formula, V−E+F=2V - E + F = 2.
For a standard rectangular prism with 88 vertices, 1212 edges, and 66 faces, this formula holds true: 8−12+6=28 - 12 + 6 = 2.