18 min read

Naming 3D Solids

Every solid can be described by its faces, edges, and vertices.

Faces, Edges, and Vertices

Example 1 — counting a cube's parts

Count the faces, edges, and vertices of a cube. 1 Faces: 6 (top, bottom, and 4 sides) 2 Edges: 12 (4 around the top, 4 around the bottom, 4 connecting them) 3 Vertices: 8 (4 on top, 4 on the bottom) Answer: 6 faces, 12 edges, 8 vertices . As a check, Euler's formula says faces + vertices - edges = 2 : 6 + 8 - 12 = 2 ✓

Example 2 — a triangular prism

Count the faces, edges, and vertices of a triangular prism. 1 Faces: 5 (2 triangular ends, 3 rectangular sides) 2 Edges: 9 (3 on each triangular end, plus 3 connecting them) 3 Vertices: 6 (3 on each triangular end) Answer: 5 faces, 9 edges, 6 vertices . Check: 5 + 6 - 9 = 2 ✓

Practice

Which solid has one flat circular face, one curved surface, and a single vertex at its apex?

Faces, Edges, and Vertices

Example 1 — counting a cube's parts

Count the faces, edges, and vertices of a cube. 1 Faces: 6 (top, bottom, and 4 sides) 2 Edges: 12 (4 around the top, 4 around the bottom, 4 connecting them) 3 Vertices: 8 (4 on top, 4 on the bottom) Answer: 6 faces, 12 edges, 8 vertices . As a check, Euler's formula says faces + vertices - edges = 2 : 6 + 8 - 12 = 2 ✓

Example 2 — a triangular prism

Count the faces, edges, and vertices of a triangular prism. 1 Faces: 5 (2 triangular ends, 3 rectangular sides) 2 Edges: 9 (3 on each triangular end, plus 3 connecting them) 3 Vertices: 6 (3 on each triangular end) Answer: 5 faces, 9 edges, 6 vertices . Check: 5 + 6 - 9 = 2 ✓

Practice

Which solid has one flat circular face, one curved surface, and a single vertex at its apex?