Introduction

This page offers access to a curated set of materials supporting the Encyclopedia of Poly Geometry (EPG). The downloads are organized into three categories:

1. PDF documents covering all major sections of the Encyclopedia. Together, these files represent a near-complete reference set for the EPG:
   • EQF (Quadri Geometry)
   • EPG (n-Geometry, including Penta, Hexa, Hepta, etc.)
   • Conics (focusing on lesser-known items)
   • Cubics (general overview of third-degree curves)
2. Macro files for Cabri II — a dynamic geometry software package. Each macro is bundled in a zip file by geometry type. Upon installation, pressing F1 reveals the expected input parameters (e.g., I: A,B,C) and the resulting output (e.g., O: X2).
3. Mathematica Notebooks containing standard EPG modules. These files offer fast computational tools for identifying EPG items. Currently, notebooks are available for n-Geometry and are grouped by geometry type in zip archives.

Note: While every effort has been made to ensure the accuracy and functionality of these materials, occasional errors or technical inconsistencies may occur. For the macros and notebooks, no guarantees are given for correctness or operability. Users are encouraged to report issues via the forum or contact form.

Downloads

1. PDF files by section of the Encyclopedia of Poly Geometry

• Section EQF (Quadri Geometry)
• Section EPG (n-Geometry, including Penta Geometry, Hexa Geometry, etc.)
• Section Conics (focusing on lesser-known items)
• Section Cubics (general overview of third-degree curves)

2. Macros for use with the Cabri II drawing software

These macro sets were compiled by the author of the Encyclopedia of Poly Geometry and this website, and are designed to support n-Geometry constructions in Cabri II.

• Triangle Geometry macros (over 1,000 ETC-points and lines)
• Quadri Geometry macros
• Penta Geometry macros
• Hexa Geometry macros
• Hepta Geometry macros
• Octa Geometry macros
• Nona Geometry macros

Additionally, a special set of macros originally created and described by Roger Cuppens (see [63]) is included. These macros complement his work on conics and cubics and are shared here as a tribute to his contributions. Roger Cuppens is believed to have passed away around 2018. According to someone who knew him personally, “I’m sure he would have been happy to hear someone still cares about his works. I think it’s a good idea and a kind of tribute to him if you include these modules.”

No commercial use is intended, and attribution is preserved.

• Cuppens macros on conics and cubics

If a macro does not work properly, check whether its filename ends with .mac. If not, simply add .mac to the filename.

3. Mathematica Notebooks with standard EPG modules

To work with Mathematica, two notebooks serve as essential starting points:

• Baricentricas.nb
• Proyectivas.nb

Both were developed by Francisco Javier García Capitán. The first is available via his personal website, while the second was created especially for the author of this site and can be downloaded directly here.

Each notebook contains numerous modules for handling and computing geometric constructions. The code is written in Spanish, but since it’s technical Spanish, it’s easy to get used to.

As their names suggest, the first notebook is based on computations using barycentric coordinates, while the second is based on projective coordinates — that is, Cartesian coordinates extended with a third ordinate, which is either 0 (for a point at infinity) or 1 (for a finite point).

Note: For computations that rely on modules from either of these notebooks, it is sufficient to open the notebook and activate it using Evaluate Notebook. After that, a new notebook can be opened to carry out the desired calculations.

Further notebooks:

• Notebook containing Perspective Fields modules
• Notebook containing n-Geometry modules

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