Tuesday, September 23, 2025

 Building Archimedean Solids and Platonic Solids: the easy way

Let the lights of the Cosmos generate the geometry of the solids, said Plato

There have been thousands of mathematical pages written on the Archimedean solids and the Platonic solids. However, there has not really been any published work on how to build the Archimedean solids and Platonic solids. This book is the most comprehensive work ever published on how to construct the Archimedean solids and the Platonic solids.

The field of polyhedral geometry, a foundational branch of mathematics, relies on a precise set of terminology to describe the spatial relationships and properties of three-dimensional forms.

Unfortunately, the foundational branch of mathematics for polyhedral geometry does not include the terminology of carpenters who, for centuries, built the Archimedean solids without the aid of mathematics.

Whether you’re building hollow solids or skeletal solids, this book includes miter angles, blade tilt angles, diagrams, and templates to help you make these solids either as hollow solids or as skeletal solids.

This book utilizes geometry to draw out the vertex for each polyhedron, thereby obtaining the dihedral angle and edge bevel angles. No math is required. 

This book is a PDF file containing over 40 table saw sled templates for printing, as well as 382 pages of detailed techniques and instructions. Taking the guesswork out of building the solids. 

 This purchase also includes Posters.PDF download, and Pythagorean Brotherhood Descendants Math Notes PDF download.
Buy for the low price of $39.95


Purchase the book as a PDF file for $39.95




Let no one ignorant of Geometry enter, said Plato



da Vinic's Polyhedra Φ Project

Golden Rectangle Rhombicosidodecahedron

Φ Rhombicosidodecahedron



Archimedean Solid Fish Tanks


Archimedean Solid Solar Lights with Light Refraction

Roman Dodecahedrons

Platonic Solids as Hollow Solids

Platonic Solids as Skeletal Solids

Archimedean Solids as Skeletal Solids with easy-to-follow table saw sleds


Wooden Polyhedra: Precision Construction Techniques
Mastering Mathematical Beauty Through Advanced Table Saw Work
Introduction
The construction of polyhedra in wood is a testament to the union of mathematical elegance and practical craftsmanship. These intricate forms, defined by their precise geometric properties, present a unique challenge to woodworkers, requiring not only a deep understanding of geometry but also mastery of the tools and techniques that enable flawless execution. This book is designed to guide both novice and advanced woodworkers through the demanding process of building wooden polyhedra, focusing on the meticulous setting of miter and bevel angles on a table saw, the use of specialized jigs, and the essential skills needed for perfect assembly.

Understanding Polyhedral Geometry
Polyhedra are three-dimensional shapes bounded by flat polygonal faces, with the regular vertices and irregular vertices, including the Platonic solids (such as cubes, tetrahedra, and dodecahedra) and Archimedean solids. Each face must meet its neighbors at precise angles, and every edge and vertex must be carefully accounted for in the design and construction process. Before beginning, familiarize yourself with the geometry of your chosen polyhedron—study its faces, edges, and required angles, as this will inform every step of your woodworking plan.

Translating Geometry to Woodworking
The leap from geometric diagram to physical wood requires accurate calculation of both miter angles (the angle at which two pieces meet) and bevel angles (the tilt of the saw blade to match the polyhedral faces). For example, constructing a dodecahedron involves cutting twelve identical pentagonal faces, each meeting at precise dihedral angles. Calculating these angles is crucial; this book includes all the necessary mathematical references and woodworking calculations to determine the exact settings for your table saw.

Utilizing Table Saw Sleds Templates
Table saw sleds are indispensable for polyhedral construction. A well-designed sled stabilizes your workpiece and maintains consistent angles for repeated cuts. For complex polyhedra, the templates included in this book required toggle clamps to hold pieces at unusual angles. Build these table saw sleds from stable materials and verify their accuracy before use.
Techniques for Flawless Assembly
Achieving a seamless fit across the many joints of a polyhedron is the ultimate test of woodworking precision. Here are essential assembly techniques:
Dry Assembly: Before gluing, assemble all pieces to ensure a proper fit. Minor adjustments can be made with sanding blocks or shooting boards.
Clamping Strategies: Use band clamps, rubber bands, or custom jigs to hold pieces together without distorting the angles.
Glue Selection: Choose a wood glue with a reasonable open time to allow for careful positioning. I use Titebond III
Finishing Touches: After assembly, sand lightly to remove any small imperfections, being careful not to alter the angles at the edges of the polygon faces.

Challenges and Mastery
Polyhedral woodworking is not for the faint of heart. Even a deviation of a few degrees can result in visible gaps that compromise both the structural and aesthetic integrity of the final piece. This book serves as both a challenge and a benchmark for advanced woodworking skills, pushing the limits of a table saw’s accuracy and the craftsman’s attention to detail. Mastery is signified not only by the completion of the polyhedral but by the pursuit of perfection in every joint and surface.

Final Words on this book
Constructing wooden polyhedra is a journey through mathematical art and technical mastery. By following the guidance in this book—calculating angles precisely, mastering saw setups, and executing flawless assembly—you will unlock new levels of woodworking skill and create captivating pieces that celebrate both geometry and craftsmanship.

Purchase the book as a PDF file for $39.95


















Monday, September 8, 2025

Dodecahedron Fish Tank

Platonic Solid Dodecahedron

Faces

12 Pentagons 

Edge Length 4.5"

1/4" Fluorescent Neon Acrylic Plexiglass: Green




Use the scribe template to scribe and cut a piece of wood with a 31.71° angle.


Use the scribe block to set the table saw blade tilt to 31.71°.


Edge bevel one edge ofthe material. Then, use the polygon table saw sled to edge-bevel another edge. Set a stop block to cut all 12 pentagon faces to the same length. 


Next, mark off the desired edge length of the pentagon faces and set a stop block. 


Continue rotating the material until all the pentagon edges are beveled. 







Glue and assemble 





The Dodecahedron can also be used for a flower pot, light shade, or lamp. 











Friday, September 5, 2025

  Rhombicuboctahedron  Fish Tank

Archimedean Solid Small Rhombicuboctahedron 

Faces

18 Squares

8 Equilateral Triangles

Polygon Saw Blade Bevel Angles

Square: 22.5°

Equilateral Triangle: 12.76°

Edge Length 3"

1/2" Polycarbonate material







Use the table saw scribe templates to scribe and cut the blade tilt blocks to 22.5° and  12.76°.




Set the table saw blade tilt to 22.5° for the square faces.


Bevel both edges of the material to a 3" width. Then edge bevel the end of the material. 


Cut the material into 6 1/2" pieces with an edge bevel at each end of the material. 


Then set a stop for the 3" width.


Cut all of the squares to a 3" square.







Set the table saw blade tilt to 12.76° for the Equilateral Triangles.



Edge bevel both edges of the material for the Equilateral Triangles. With the bevels being parallel. 

Bevel the end of the material. 


Lay out the Equilateral Triangles and make the cut so that the cut-off looks like a rhombus. 


Next, mark off the width of the Equilateral Triangle so it is the exact same width as the squares. 


Finish cutting the Equilateral Triangles with the table saw polygon sled. 


Tape the pieces together for the bottom of the Rhombicuboctahedron net.



Tape the entire bottom half of the Rhombicuboctahedron.


Turn the bottom of the Rhombicuboctahedron over and glue the pieces together. 


Tape up the top of the Rhombicuboctahedron.



Cut the tape around the top square of the Rhombicuboctahedron and remove the square. You can now glue the remaining pieces of the Rhombicuboctahedron together.














Wednesday, September 3, 2025

 Icosidodecahedron Fish Tank

Archimedean Solid Icosidodecahedron

Faces

12 Pentagons 

20 Equilateral Triangles

Edge Length 2.75"

1/2" Polycarbonate material





Dihedral Angle
142.62263°
Polygon Saw Blade Bevel Angles
Equilateral Triangle: 10.8123169°
Pentagon: 26.56505°

Set the table saw blade tilt to 26.57° for the pentagon faces.

Rip the 1/2" polycarbonate to 5" in width with the edge bevel.


Cut the material into 5" pieces. Then use the Pentagon table saw sled to bevel one edge. The previous bevel is against the stop with the edge bevel facing up. Set a width, a stop, and a toggle clamp to cut all 12 pieces to the same width. 


Then lay out one edge at 2.75" and place a stop with a toggle clamp to cut all of the pieces at the same width.

Rotate the pieces and cut all of the edges. 


Cutting the  20 Equilateral Triangles. 

Set the table saw blade tilt to 10.81° for the Equilateral Triangles. 

Rip the material to about 3" with the edge bevels being parallel.

Lay out two triangles and cut the material to form a rhombus. 


Lay out one edge of the material at 2.75" and set a width stop with the toggle clamp. 




Cut the triangles. 





Glue up 




Tape up a top and bottom. They will be identical. 

Tape the two pieces together. 

Cut the tape at the top pentagon face and remove it. Then glue the pieces together on the inside of the Icosidodecahedron.