Roof Framing Geometry

Thursday, April 23, 2026

RafterTools Updates

RafterTools Books on Geometry, Stereotomy, and Trigonometry.

https://www.raftertools.com/

HG I-II Holy Grail of Roof Framing Geometry & Trigonometry

HG III The Art of the Line for Carpentry Stereotomy Geometry

HG IV Circular Work in Carpentry Stereotomy Geometry

HG V Twisted Circular Work in Carpentry Stereotomy Geometry

HG VI American Trestle Study Pro Stereotomy Geometry

HG VII Building Archimedean Solids and Platonic Solids

RafterTools+ Dark iPhone

Here's a link to the Raftertools+ Dark website: 14 Roof Framing calculators

https://www.raftertools.com/dark/

A comprehensive suite of roof framing calculators covering equal pitch, irregular hip roofs, polygon roofs, timber framing, bay windows, barrel dormers, eyebrow dormers, round towers, elliptical rafters, groin vaults, and more.

In the evolving world of carpentry, mastering roof framing requires precision, deep knowledge, and the right tools. RafterTools+ Dark is designed to elevate both apprentices and seasoned carpenters by providing a comprehensive suite of calculators and resources that ensure confidence and accuracy in every project.

To truly thrive as a professional carpenter today, you need more than top-notch equipment—you need digital support. The RafterTools+ Dark app complements your toolkit, empowering you to transition from apprentice to journeyman or become the most knowledgeable rough-framing carpenter on any jobsite.

Roof Framing Help Desk iPhone

Here's a link to the Roof Framing Help Desk website

https://www.raftertools.com/bot/

Over 300+ Techniques to choose from.

Expertise in Roof Framing Techniques From Around the World

At Roof Framing Help Desk, we specialize in advanced roof framing techniques. Our expertise includes calculating rafter angles for various roof types, ensuring precision, and a knowledge database of keywords linked to web pages, PDF files, and YouTube videos with roof framing techniques.

The Roof Framing Help Desk app is designed to be a community project similar to Wikipedia. Currently, there are more than 300 keywords to search, 150+ webpages, and over 800 drawings.

Whether it's an irregular Hip Roof, Octagon Roof, Polygon Roof, or a Standard Pitched Roof, the Roof Framing Help Desk app can help you with your roof framing techniques.

Roof Framing Help Desk Android

RPN Carpenters Calc iPhone

Here's a link to the RPN Carpenters Calc website

https://www.raftertools.com/dark/carpenter.html

This Carpenter's Calculator is a Reverse Polish Notation (RPN) calculator, typically an engineering or financial calculator that uses postfix notation. However, this calculator is designed for carpenters and builders, and includes functions specific to construction calculations such as rafter lengths, angles, stair calculations, and more. It also includes standard mathematical functions and basic arithmetic operations. The RPN input method allows quick, efficient calculations without parentheses, making it ideal for on-site use where speed and accuracy are important. Example calculations and instructions for using the various functions of the Carpenter's Calculator are provided below.

I've used the HP 48g & HP 50g calculator since the the 1980's for rafter calculations. So, I designed this calculator to have a similar feel and functionality to those calculators, but with a more modern interface and additional functions specific to carpentry and construction.

Stair Tangent Dark iPhone

Here's a link to the Stair Tangent Dark website: 12 stair calculators

Calculators cover stringers, risers, circular stairs, elliptical stairs, winders, arch radius, and more.

https://www.stairtangent.com/

Professional Stair Builders don't need an app to build stairs; they just know how. This app is for rough-frame carpenters who don't build stairs every day but could use a stair-building calculator to check their calculations.

Build a set of stairs that you are gonna be proud of. With Stair Tangent Dark, you can eliminate cumulative math errors when building or constructing stairs.

With the Elliptical Stairs calculations and Ellipse Point Layout for X-Y plotting, you can rival any professional stair builder's capabilities.

Crown Tools Dark iPhone

Here's a link to the Crown Tools Dark website: 15 crown molding calculators

https://www.crownmoldingtools.com/

Crown Tools Dark is an app with functions to calculate complex crown miter and bevel angles that other calculators don't offer.

Crown Molding Miter Angle and Saw Blade Bevel Angles

Cathedral ceiling rake crown molding, miter and bevel angles

Vaulted ceiling rake, crown molding, miter, and bevel angles

Rake Crown Molding Miter and Bevel Angles

Polygon Crown Molding Miter and Bevel Angles

Radius BullNose Crown Molding Miter and Bevel Angles and width

Horizontal to Rake Crown Molding Miter and Bevel Angles

Calculate Crown Molding Spring Angles

Calculate Horizontal to Rake Wall No Transitions

Calculate Rake Wall To Horizontal at Corner Wall No Transitions

Calculate Rake Crown to Rake Crown No Transitions

Calculate Rake To Level No Transitions

Calculate Rake To Level Return No Transitions

Calculate Rake To Rake at Peak No Transitions

Calculate Exterior Rake Molding using 3 Different Crown Molding Profiles

Included with all apps.

Have some fun with the screen animation. Select your own image to animate or use one of the ten included animation .png files. Like dirt bike, windsurfing, speed boat, sail boat, and some carpenters too

Monday, March 30, 2026

Roof Framing Help Desk app for iPhone

The Roof Framing Help Desk app/Bot is designed to serve as a knowledge base for roof framing techniques and to calculate rafter angles and rafter lengths. It can calculate the rafter angles for equal-pitched, unequal-pitched, and polygon roofs, such as Octagon roofs. It is also a knowledge base for roof framing. Enter a keyword like 'irregular hip roof,' and it will provide you with a link to a web page with explanations on laying out an irregular hip roof. Or enter a keyword like devioement-hip shift, and it will provide you with a link to a webpage for devoiement. Or how to lay out a hip rafter precisely.

There are currently over 300 keywords to search the knowledge database. Over 800 drawings explaining different roof framing techniques, as well as 150 new webpages of information for the keywords in the knowledge database. If you have a webpage, PDF file, or YouTube video you would like to share, you can add it to the knowledge database. The main concept of the knowledge database is to make it similar to Wikipedia, except for roof framing techniques.

Use the built-in rafter length calculator for irregular hip roofs. Include the hip rafter offset calculations for equal overhang.

Download the app on Apple Store
Roof Framing Help Desk app

Roof Framing Help Desk Rafter Length Calculator

Eave Angle: 30-160 degrees, usually 90°
Main Rafter Run: The horizontal distance from the wall plate to the ridge
Main Rafter Pitch: 1-24 roof pitch, or enter the roof slope angle
Adjacent Rafter Pitch: 1-24 roof pitch, or enter the roof slope angle
Hip Rafter Width: The width of the hip rafter: 1-1000
Ridge Width: The width of the ridge
Jack Rafter Width: The width of the jack rafter
Jack Rafter Spacing: Jack Rafter On Center Spacing
Overhang Run: The horizontal distance from the wall plate to the end of the overhang
With the Option to use Hip Rafter Shift: The default is not to use hip rafter shift
With the Option to enter Roof Slope Angles instead of Pitch: 1-89 degrees
With the Option to to display the output in inch or decimal format: The default is to display in inch format
With the Option to calculate the Jack Rafter Length for the first Jack Rafter from the Shortest or Longest Jack Rafter: The default is to calculate from the Shortest

https://www.raftertools.com/bot/rafter-calculator.html

Friday, December 12, 2025

Twisted Spires Book V

HG Twisted Circular Work in Carpentry Stereotomy Geometry
Dome Tours & Arrow Torus
Dome Tors & Flèche Torse
Canted Twisted Spires
Plumb Twisted Spires
Twisted Cones
Canted Spirals
Twisted Bell Towers
Rhombicosidodecahedron
Icosahedron
Parallogram Technique

This 400-page hardcover book, $145.00, also includes a USB Flash Drive of 2GB of (100+) templates and drawings that you can print at a 1:1 scale and 20 videos showing how to lay out, cut, and shape the twisted spire rafters.

This is the most comprehensive book ever written on twisted spires.

Ships on 12-26-2025: Price includes Shipping

First Edition
ISBN 9798317828257

Link to purchase the book

Video of page 2 from the new book Twisted Circular Work

Video of page 3 from the new book Twisted Circular Work

Video of page 4 from the new book Twisted Circular Work

Video of page 5 from the new book Twisted Circular Work

Video of page 6 from the new book Twisted Circular Work

Video of page 7 from the new book Twisted Circular Work

Video of page 8 from the new book Twisted Circular Work

Video of page 9 from the new book Twisted Circular Work

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.