Catalogue of Polypennies

Introduction

A polypenny is a figure made of equal discs joined tangentially. Polypennies are identified by plane homeomorphism: continuous deformation of the plane. Free polypennies may be reflected; one-sided polypennies may not.

Polypennies may also be distinguished by internal homeomorphism without reference to the plane. Alexandre Owen Muñiz gives this example of two homeomorphic polypennies that are not homeomorphically embedded in the plane:

Polypennies may also be distinguished by isomorphism of their adjacency graphs without respect to the cyclical sequence of adjacencies at each node. These polypennies have isomorphic adjacency graphs and are not internally homeomorphic:

This page shows all free polypennies of orders 1–6. Erich Friedman enumerated all polypennies up to order 4. Alexandre Owen Muñiz enumerates polypennies up to order 5 on Flexible Polyforms at his site Math at First Sight.

The On-Line Encyclopedia of Integer Sequences enumerates connected penny graphs (not polypennies) up to order 8 as sequence A085632.

Enumeration

OrderFreeOne-Sided
111
211
322
455
51313
64657

Monopenny

Dipenny

Tripennies

Tetrapennies

Pentapennies

Hexapennies


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Col. George Sicherman [ HOME | MAIL ]