# Polyfett Irreptiles

## Introduction

A *polyfett* is a plane figure
formed by joining equal isosceles right triangles on the quadrille grid
at vertices or equal edges.
Polifetti are a generalization of polyaboloes.
See Catalogue of Polyfetts.
An *irreptile* is a geometric shape that can be divided into
smaller pieces, not necessarily equal, with the same shape as the original.

The term *irreptile* was coined by Dr. Karl Scherer,
who studied such tilings extensively.
His results appear in chapters
3 and 4 of his book *A Puzzling Journey to the Reptiles
and Related Animals,* and in some of his Wolfram Demonstrations, notably
Irreptiles
and
Some
Irreptiles of Order Greater Than 20.

Erich Friedman's Math
Magic for October 2010 presents
irreptilings for polykings and polymings, which are also vertex-connected
polyforms.

Here I present minimal known irreptilings for proper polyfetts—those
that are not also polyaboloes.
Polyfetts with the same shapes as smaller polyfetts are omitted.
Proper reptilings are shown in shades of blue.

See also Polyabolo Irreptiles.

### No Solution

### No Solution

### No Known Solution

Last revised 2020-09-26.

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Col. George Sicherman
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