# Scaled Polyiamond 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 polyiamond that can form standard tetrads has three cells.

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

Here I show the smallest known scaled
tetrads for polyiamonds with up to 7 cells.
If you find a smaller solution or solve an unsolved case, please write.

See also Scaled Polytan Tetrads.

## Key

## Triamond

## Tetriamonds

## Pentiamonds

## Hexiamonds

### Holeless Variants

## Heptiamonds

Last revised 2023-05-18.

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Col. George Sicherman
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