Solved cryptogram
There are exactly five perfectly regular solids, and no arrangement of geometry allows a sixth.
Mathematics Facts, sourced to Wolfram MathWorld.
What it means
The tetrahedron, cube, octahedron, dodecahedron and icosahedron exhaust the possibilities. The reason is simple enough to state: at least three faces must meet at each corner, and their angles must add to less than a full turn or the shape cannot close up. Working through the identical regular polygons that satisfy both conditions leaves five options and no others.
The claim comes from Wolfram MathWorld, and the page it comes from was read on 2026-08-27 to confirm it still says this.
This is not the kind of claim that goes out of date, which is why it was set as a puzzle rather than a fact with a shelf life.
Solve it yourself
This fact is a cryptogram here: 79 letters over 21 different ones, graded medium.
- SourceWolfram MathWorld
- CollectionMathematics Facts
- Difficultymedium
- Length79 letters, 21 of them different
Nearby in the collection
The facts either side of this one.
- Wolfram MathWorldhard, 65 letters
- Wolfram MathWorldmedium, 75 letters
- Wolfram MathWorldmedium, 81 letters
- Wolfram MathWorldhard, 79 letters
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Scored closest to it by the model behind our guide to solving cryptograms.
- Wolfram MathWorldmedium, 70 letters
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