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Geodesic Dome Notes & Calculator

written by Rene K. Mueller, Copyright (c) 2005, 2006, 2007, last updated Sun, September 22, 2013

Updates

Sat, June 2, 2007: Changed strut sorting from 1/1'000 to 1/10'000, which changed the amount of different strut lengths for higher subdivided domes; removed two cube-based domes from the overview, now 65 variants featured.

Wed, May 30, 2007: Included bending angle αlath for all struts and angles of face triangles for each version of dome.

Tue, April 24, 2007: Added Octahedron L4 3/8, 5/8 dome and L3 7/16, 9/16 variants, as well Rhombicuboctahedron based domes (1V/L1, 2V/L2, and L3 at 3/8 & 5/8 height), total of 67 variants now featured.

Mon, April 2, 2007: Major rewrite of the entire notes, I cover following geodesic dome variants (57) of Icosahedron (1V to 8V and related), Octahedron (1V to 10V and related), Cuboctahedron (1V to 4V), Cube (1V to 8V and related), and finally Truncated Octahedron (1V to 4V and related) fow now. Be aware of new notion of strut types (A-F etc so are labeled new).

Sat, January 20, 2007: Minor update on Icosahedron, and 2nd level floor options included.

Wed, February 22, 2006: Added 4/8 sphere cover calculator taken from Wigwam-section, and photos of the.

Tue, September 13, 2005: More photos of the 4V model.

Sun, September 11, 2005: Added 4V Model photos.

Wed, September 7, 2005: On the fly rendering of dome sketch (incl. human height comparison).

Mon, September 5, 2005: Added cover Acover information.

Sat, September 3, 2005: Added 4V 4/8 Dome information. Added more infos on Real Life Application.

Thu, August 25, 2005: Real Life Application notes added, about cover and such.

Sun, August 14, 2005: First version, with 2V 4/8 and 3V 3/8 & 5/8 Sphere.

Welcome to my detailed and comprehensive geodesic domes notes, actually the 2nd version (total rewrite of the 1st version). Since it has become so long I include a table of content ahead.

Table of Content

  1. Table of Content
    1. Changes
  2. Introduction
    1. Origin of the Geodesic Dome
    2. Geodesize: Triangulate & Normalize
    3. Procedure & Evolution of a Subdividing Triangle
    4. The nV Notion
    5. The Ln Notion
    6. The Concated V Notion
    7. The Concated V vs Ln Notion
    8. Normalizing
    9. References
  3. Overview of Variants
    1. Numerical Overview
    2. Amount of Struts vs. Strut Variance
    3. Amount of Struts vs. Strut Types
  4. How to Use the Notes
  5. Strut Options & Notion
    1. Wooden Strut with Flat Connector
    2. Wooden Strut with Pipe Hub
    3. Pipe/Tube based Strut
    4. Bamboo Strut
    5. Bending the Strut-Endings
    6. Detailed Calculation of the Faces or Hub/Strut Angles
  6. The Icosahedron
    1. 1V/L1 2/3 Icosahedron Dome
    2. 2V/L2 Icosahedron Dome
    3. 3V 4/9 Icosahedron Dome
    4. 3V 5/9 Icosahedron Dome
    5. 4V Icosahedron Dome
    6. L3 Icosahedron Dome
    7. 5V 7/15 Icosahedron Dome
    8. 5V 8/15 Icosahedron Dome
    9. 6V Icosahedron Dome
    10. 2V.3V Icosahedron Dome
    11. 3V.2V Icosahedron Dome
    12. 7V 10/21 Icosahedron Dome
    13. 7V 11/21 Icosahedron Dome
    14. 8V Icosahedron Dome
    15. L4 Icosahedron Dome
  7. The Octahedron
    1. 1V/L1 Octahedron Dome
    2. 2V/L2 Octahedron Dome
    3. 3V Octahedron Dome
    4. 4V Octahedron Dome
    5. L3 Octahedron Dome
    6. L3 1/4 Octahedron Dome
    7. L3 3/4 Octahedron Dome
    8. 5V Octahedron Dome
    9. 6V Octahedron Dome
    10. 2V.3V Octahedron Dome
    11. 3V.2V Octahedron Dome
    12. 7V Octahedron Dome
    13. 8V Octahedron Dome
    14. L4 Octahedron Dome
    15. L4 7/16 Octahedron Dome
    16. L4 9/16 Octahedron Dome
    17. 9V Octahedron Dome
    18. 3V.3V Octahedron Dome
    19. 10V Octahedron Dome
    20. 2V.5V Octahedron Dome
    21. 2V.5V Octahedron Dome
  8. The Cube
    1. Preparing the Cube
    2. 1V/L1 Cube Dome
    3. 2V/L2 Cube Dome
    4. 3V Cube Dome
    5. 4V Cube Dome
    6. L3 Cube Dome
    7. 5V Cube Dome
    8. 6V Cube Dome
    9. 2V.3V Cube Dome
    10. 3V.2V Cube Dome
    11. 7V Cube Dome
  9. The Cuboctahedron
    1. Preparing the Cuboctahedron
    2. 1V/L1 Cuboctahedron Dome
    3. 2V/L2 Cuboctahedron Dome
    4. 3V Cuboctahedron Dome
    5. 4V Cuboctahedron Dome
    6. L3 Cuboctahedron Dome
    7. 5V Cuboctahedron Dome
    8. 6V Cuboctahedron Dome
    9. 2V.3V Cuboctahedron Dome
    10. 3V.2V Cuboctahedron Dome
  10. The Truncated Octahedron
    1. Preparing the Truncated Octahedron
    2. 1V/L1 Truncated Octahedron Dome
    3. 2V/L2 Truncated Octahedron Dome
    4. 3V Truncated Octahedron Dome
    5. 4V Truncated Octahedron Dome
    6. L3 Truncated Octahedron Dome
  11. The Rhombicuboctahedron
    1. Preparing the Rhombicuboctahedron
    2. 1V/L1 3/8 Rhombicuboctahedron Dome
    3. 1V/L1 5/8 Rhombicuboctahedron Dome
    4. 2V/L2 3/8 Rhombicuboctahedron Dome
    5. 2V/L2 5/8 Rhombicuboctahedron Dome
    6. 3V 3/8 Rhombicuboctahedron Dome
    7. 3V 5/8 Rhombicuboctahedron Dome
  12. Building Models
    1. 3V 5/9 Icosahedron Model
    2. 2V Icosahedron Model
    3. 4V Icosahedron Model
    4. 2V/L2 Cuboctahedron Model
  13. Real Life Application
    1. Options
    2. Connectors
    3. Separate Functions
    4. Cover
    5. 4/8 Sphere Cover Calculator
    6. Sewing the Cover
    7. 4V 4/8 Geodesic Dome Model with Cover
    8. Windows & Door
    9. Interior & Floor
    10. 2nd Floor
  14. Links

Changes

Following changes were made to previous versions:
  • 2nd version: Icosahedron, Octahedron, Cube, Cuboctahedron and Truncated Octahedron for each 1V to 6V or more triangulations, a few strut cutting optimization included. Be aware the notion of the strut types of Icosahedron 2V, 3V and 4V changed from previous version of the notes.
  • 1st version: Icosahedron based domes covered in details: 2V, 3V and 4V with optimizations of cutting struts


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