Solved cryptogram
There are exactly seventeen ways to repeat a pattern across a flat wall, and no more.
Mathematics Facts, sourced to Wolfram MathWorld.
Solve it yourself
This fact is a cryptogram here: 68 letters over 18 different ones, graded medium.
Or go to the puzzle’s own page first.
What it means
The count is of symmetry types rather than of designs. Two wallpapers belong to the same type when the same combination of slides, turns, mirrors and glide reflections carries each pattern onto itself. Every repeating flat design ever made falls into one of seventeen classes, and the proof that there is no eighteenth dates from 1891. All seventeen appear in the tilework of the Alhambra, centuries before anyone counted them.
The claim comes from Wolfram MathWorld.
- SourceWolfram MathWorld
- CollectionMathematics Facts
- Difficultymedium
- Length68 letters, 18 of them different
Nearby in the collection
The facts either side of this one.
- Wolfram MathWorldmedium, 72 letters
- Wolfram MathWorldmedium, 72 letters
- On-Line Encyclopedia of Integer Sequencesmedium, 71 letters
- MacTutor History of Mathematicsmedium, 71 letters
About as hard as this one
Scored closest to it by the model behind our guide to solving cryptograms.
- Wolfram MathWorldmedium, 70 letters
- Wolfram MathWorldmedium, 75 letters
- MacTutor History of Mathematicsmedium, 72 letters
- Wolfram MathWorldmedium, 75 letters