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Faces, edges and vertices, step by step

Counting the parts of a solid is harder than it sounds, because half of them are round the back.

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The question
How many edges?

pentagonal prism: how many edges?

pentagonal prism
base:pentagon5 sides
5 + 5 + 5=15
edges:15
  1. Half of a solid is round the back. The dashed lines in the drawing are the parts you cannot see, and they count exactly the same as the ones you can — counting only what faces you is where this goes wrong, every time.
  2. Start by naming the base, because everything else is built on it. A pentagonal prism has a pentagon at the bottom, so the base has 5 sides.
  3. Edges come in three sets: 5 round one end, 5 round the other, and 5 joining the two ends together. Nothing else has an edge, so it is 5 + 5 + 5.
  4. So a pentagonal prism has 15 edges.

How it works.

  1. 01

    Half of a solid is round the back. The dashed lines in the drawing are the parts you cannot see, and they count exactly the same as the ones you can — counting only what faces you is where this goes wrong, every time.

  2. 02

    Start by naming the base, because everything else is built on it. A pentagonal prism has a pentagon at the bottom, so the base has 5 sides.

  3. 03

    Edges come in three sets: 5 round one end, 5 round the other, and 5 joining the two ends together. Nothing else has an edge, so it is 5 + 5 + 5.

  4. 04

    So a pentagonal prism has 15 edges.

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