Building Solids

Building Archimedean and Platonic Solids
Hollow and Skeletal table saw, and miter saw settings for:
 
Archimedean Solids
Truncated Tetrahedron
Cuboctahedron
Truncated Cube
Truncated Octahedron
Small Rhombicuboctahedron
Truncated Cuboctahedron
Icosidodecahedron
Snub Cube
Truncated Dodecahedron
Truncated Icosahedron
Rhombicosidodecahedron
Truncated Icosidodecahedron
Snub Dodecahedron
 
Platonic Solids
Tetrahedron
Cube
Octahedron
Icosahedron
Dodecahedron
 
Also, includes Instructions, Templates, Resources, and Settings menu selections.

Calculates the CircumRadius and Edge Length dimension for all Polyhedral

This app is basded on my book:

HG VII Building Archimedean Solids and Platonic Solids
url link https://www.raftertools.com/archimedean.html
 
Building a Wooden Polyhedral with Geometric Precision. With this app
 
 
Focuses on translating polyhedral geometry into woodworking techniques. Includes detailed instructions on setting miter and bevel angles on a table saw. Provides Polygon Sled templates for printing on 11" x 17" paper.  Emphasizes the importance of precise angle calculations for flawless assembly. Uses geometry to determine vertex dihedral and edge bevel angles without complex math. Offers techniques for building hollow and skeletal solids, including jig and sled setups. Includes formulas for diagonals of polygons and their relation to edge lengths, e.g., the golden ratio. Describes the setup of polygon-specific sleds with precise angles for accurate cuts. Emphasizes the importance of verifying angles with protractors and templates for accuracy. Provides detailed settings for compound miter saws and table saws to achieve correct dihedral angles.
  
Overview of Polyhedral Joinery and Angles
 
The app displays mathematical calculations-angles for constructing all of the Archimedean and Platonic solids, focusing on precise joinery, saw blade angles, for Hollow Solids or Skeletal Solids.
 
Calculation Methods for Polyhedral Angles
 
 
Angles are derived using cosine functions, dihedral angles, and polygon footprint angles. The Hip Rafter Backing Angle (B) and Jack Rafter Side Cut Angle (E) are calculated with trigonometric functions. Development begins with the dihedral angle between polygonal faces on roof surfaces. Specific formulas, such as arcsine, arctan, and their combinations, are used to find plan, slope, and face angles. Examples include calculations for Snub Cube, Truncated Cuboctahedron, and other Archimedean solids with dihedral angles ranging from approximately 12.45° to 153.23°.
 
 
Roof Framing and Joinery Angles
 
The app details the calculations for hip rafter and profile rafter angles using trigonometry. Then, the angles of the table saw and miter saw are used to cut the material for the solids.
 
Eave angles are derived from polygon footprint angles and dihedral angles. Roof surface and plan view angles are used to determine rafter slopes and backing angles. Specific angles for cutting rafters with miter and bevel settings are provided, e.g., 54.74°, 35.26°, 18°, and 30°. Dihedral angles between roof faces are used to set saw blade tilt and miter angles for precise joinery. Techniques include using table saw sleds, compound miter saws, and templates for accurate cuts.
 
Construction Techniques for Polyhedral
 
Use of specific saw blade tilt angles and edge bevel angles for each face type. Cutting involves setting saws at precise angles, using templates, stops, and sleds. Assembly often requires gluing, taping, and pinning for stability. Special techniques include nested build methods, the use of templates printed at 1:1 scale, and the creation of skeletal or hollow models. Examples include fish tanks, light refraction models, and artistic sculptures. Dihedral angles vary from approximately 12.45° to 153.23°. Polygon diagonals are listed, e.g., pentagon (1.61803), octagon (1.84776). Saw blade tilt and bevel angles are tailored for each face type to ensure precise joinery.