# Scaled Polytan Tetrads

## Introduction

In plane geometry, a *tetrad* is an arrangement of four congruent
shapes in which each borders the other three.
See Polyform Tetrads.
At his website Atlantis, Dr. Karl Scherer introduced *similar*
or *scaled tetrads.*
These are arrangements of four similar shapes in which each borders the
other three.

In general, scaled tetrads are easier to find that standard tetrads.
Scherer's page showed how the right tromino can form scaled tetrads.
The smallest polyominoes that can form standard tetrads have eight cells.

Scherer proved that convex shapes cannot form tetrads.
However, some can form scaled tetrads, as shown below.

Here I show the smallest known scaled
tetrads for polytans with 3, 4, or 5 cells,
using scale factors that are integers or integer multiples of √2.
If you find a smaller solution or solve an unsolved case, please write.

## Tritans

### Unsolved

## Tetratans

### Unsolved

## Pentatans

### Unsolved

Last revised 2018-11-11.

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Col. George Sicherman
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