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Müller Geodesic Solitude Johnny's Capsule Geodesic Clay Mud Dome Jurtendorf (Switzerland) Neolithics of Pfyn Strawbale Cabin Dome Geodesic Dome Geodesic Dome Notes & Calculator Table of Content Introduction Overview of Variants How to Use the Notes Strut Options & Notion The Icosahedron The Octahedron The Cube The Cuboctahedron The Truncated Octahedron The Rhombicuboctahedron Building Models Real Life Application Links Geodesic Dome Diary Geodesic Polyhedra Polyhedra Notes Bow Dome Triangulated Bow Dome Star Dome Star Dome Diary Wigwam Zome Helix Zome Low Cost Dome (PVC) Miscellaneous Domes Site Search Enter term & press ENTER If you found the information useful, consider to make a donation:   Page << Prev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | Next >> Geodesic Dome Notes & Calculator written by Rene K. Mueller, Copyright (c) 2005, 2006, 2007, last updated Tue, January 29, 2019 Overview of Variants Since the possibilities are so vast I have selected a couple of platonic and archimedean solids - as I previously studied in Geodesic Polyhedra - which seem reasonable for dome constructions, and created variants with up 1000 struts, and max 30 different strut lengths. So, these are the results: Icosahedron-based Geodesic Domes 1V 2/3 25 struts (1 kind) 2V 65 struts (2 kinds) 3V 4/9 120 struts (3 kinds) 3V 5/9 165 struts (3 kinds) 4V 250 struts (6 kinds) L3 250 struts (5 kinds) 5V 7/15 350 struts (9 kinds) 5V 8/15 425 struts (9 kinds) 6V 555 struts (9 kinds) 2V.3V 555 struts (10 kinds) 7V 10/21 700 struts (15 kinds) 7V 11/21 805 struts (15 kinds) 8V 980 struts (19 kinds) L4 980 struts (14 kinds) Octahedron-based Geodesic Domes 1V 8 struts (1 kind) 2V 28 struts (2 kinds) 3V 60 struts (3 kinds) 4V 104 struts (6 kinds) L3 104 struts (5 kinds) L3 3/8 60 struts (5 kinds) L3 5/8 144 struts (5 kinds) 5V 160 struts (9 kinds) 6V 228 struts (9 kinds) 2V.3V 228 struts (10 kinds) 3V.2V 228 struts (7 kinds) 7V 308 struts (16 kinds) 8V 400 struts (20 kinds) L4 400 struts (15 kinds) L4 7/16 308 struts (15 kinds) L4 9/16 488 struts (15 kinds) 9V 504 struts (18 kinds) 3V.3V 504 struts (15 kinds) 10V 620 struts (30 kinds) 2V.5V 620 struts (28 kinds) 5V.2V 620 struts (24 kinds) Cube-based Geodesic Domes 1V 21 struts (2 kinds) 2V 78 struts (4 kinds) 3V 171 struts (10 kinds) 4V 300 struts (14 kinds) L3 300 struts (11 kinds) 5V 465 struts (21 kinds) 6V 666 struts (29 kinds) 2V.3V 666 struts (27 kinds) 3V.2V 666 struts (22 kinds) 7V 903 struts (42 kinds) Cuboctahedron-based Geodesic Domes 1V 27 struts (2 kinds) 2V 102 struts (5 kinds) 3V 225 struts (10 kinds) 4V 396 struts (18 kinds) L3 396 struts (15 kinds) 5V 615 struts (28 kinds) 6V 882 struts (36 kinds) 2V.3V 882 struts (34 kinds) 3V.2V 882 struts (28 kinds) Truncated Octahedron-based Geodesic Domes 1V 60 struts (4 kinds) 2V 228 struts (7 kinds) 3V 504 struts (15 kinds) 4V 888 struts (25 kinds) L3 888 struts (19 kinds) Rhombicuboctahedron-based Geodesic Domes 1V 3/8 40 struts (2 kinds) 1V 5/8 88 struts (2 kinds) 2V 3/8 152 struts (5 kinds) 2V 5/8 344 struts (5 kinds) 3V 3/8 336 struts (10 kinds) 3V 5/8 768 struts (10 kinds) Numerical Overview In order to assist to overview the options further, consider to study following table carefully, it's worth it. Types: strut types or amount of different strut lengths, the lesser the better Variance: strut variance, difference between longest and shortest strut, the lesser the better (more even triangles) The L-variant is better than the comperable V-variant, in sense of strut variance and amount of different struts. The list is sorted by the amount of struts, so you can choose how complex the dome should become. Name Connectors Faces Struts Types Variance Octahedron 1V 5 4 8 1 0% Cube 1V 10 12 21 2 25.6% Icosahedron 1V 2/3 11 15 25 1 0% Cuboctahedron 1V 12 16 27 2 30.7% Octahedron 2V 13 16 28 2 30.7% Rhombicuboctahedron 1V 3/8 17 24 40 2 36.5% Octahedron 3V 25 36 60 3 46.1% Octahedron L3 3/8 25 36 60 5 48.0% Truncated Octahedron 1V 25 36 60 4 46.1% Icosahedron 2V 26 40 65 2 13.1% Cube 2V 31 48 78 4 37.4% Rhombicuboctahedron 1V 5/8 33 56 88 2 36.5% Name Connectors Faces Struts Types Variance Cuboctahedron 2V 39 64 102 5 48.0% Octahedron 4V 41 64 104 6 80.2% Octahedron L3 41 64 104 5 48.0% Icosahedron 3V 4/9 46 75 120 3 18.3% Octahedron L3 5/8 53 92 144 5 48.0% Rhombicuboctahedron 2V 3/8 57 96 152 5 44.9% Octahedron 5V 61 100 160 9 92.9% Icosahedron 3V 5/9 61 105 165 3 18.3% Cube 3V 64 108 171 10 50.1% Cuboctahedron 3V 82 144 225 10 51.2% Octahedron 2V.3V 85 144 228 10 51.2% Octahedron 3V.2V 85 144 228 7 53.5% Name Connectors Faces Struts Types Variance Octahedron 6V 85 144 228 9 95.4% Truncated Octahedron 2V 85 144 228 7 53.5% Icosahedron 4V 91 160 250 6 28.3% Icosahedron L3 91 160 250 5 17.8% Cube 4V 109 192 300 14 56.9% Cube L3 109 192 300 11 41.5% Octahedron 7V 113 196 308 16 107.9% Octahedron L4 7/16 113 196 308 15 53.8% Rhombicuboctahedron 3V 3/8 121 216 336 10 46.2% Rhombicuboctahedron 2V 5/8 121 224 344 5 44.9% Icosahedron 5V 7/15 126 225 350 9 32.1% Cuboctahedron 4V 141 256 396 18 60.2% Name Connectors Faces Struts Types Variance Cuboctahedron L3 141 256 396 15 53.8% Octahedron 8V 145 256 400 20 112.6% Octahedron L4 145 256 400 15 53.8% Icosahedron 5V 8/15 151 275 425 9 32.1% Cube 5V 166 300 465 21 58.9% Octahedron L4 9/16 173 316 488 15 53.8% Octahedron 3V.3V 181 324 504 15 55.1% Octahedron 9V 181 324 504 18 113.2% Truncated Octahedron 3V 181 324 504 15 55.1% Icosahedron 2V.3V 196 360 555 10 18.9% Icosahedron 6V 196 360 555 9 33.2% Cuboctahedron 5V 216 400 615 28 62.8% Name Connectors Faces Struts Types Variance Octahedron 10V 221 400 620 30 119.3% Octahedron 2V.5V 221 400 620 28 62.8% Octahedron 5V.2V 221 400 620 24 98.1% Cube 2V.3V 235 432 666 27 44.4% Cube 3V.2V 235 432 666 22 52.3% Cube 6V 235 432 666 29 63.1% Icosahedron 7V 10/21 246 455 700 15 36.5% Rhombicuboctahedron 3V 5/8 265 504 768 10 46.2% Icosahedron 7V 11/21 281 525 805 15 36.5% Cuboctahedron 2V.3V 307 576 882 34 54.6% Cuboctahedron 3V.2V 307 576 882 28 53.6% Cuboctahedron 6V 307 576 882 36 63.1% Name Connectors Faces Struts Types Variance Truncated Octahedron 4V 313 576 888 25 58.0% Truncated Octahedron L3 313 576 888 19 55.6% Cube 7V 316 588 903 42 64.0% Icosahedron 8V 341 640 980 19 37.7% Icosahedron L4 341 640 980 14 19.0% Note: all strut lengths have been sorted by 1/10'000th or +/-0.00005 exact Amount of Struts vs. Strut Variance Amount of Struts vs Strut Variance Note: Click on the graphic, and click "full scale" or scroll down, and press "Print" link at the bottom of the page. In the graphic you actually see why the Icosahedron looks best, it has the least strut variance, which is an indication of more or less similiar triangles through the entire structure. And as realized before, the Ln variants additionally provide better results than the nV counterparts. The Octahedron variants, on the other hand, have high strut variances as seen above. I personally like the Cuboctahedron variants, but they have more strut variance than the Icosahedron, in other words, at the end it's your personal choice and favours which lead you to choose a polyhedral geodesic dome variant, the list above and this graphic may just assist you in your overall considerations. Amount of Struts vs. Strut Types Amount of Struts vs Strut Types Note: Click on the graphic, and click "full scale" or scroll down, and press "Print" link at the bottom of the page. In this graphic above the Icosahedron does quite well, with low amount of strut lengths, and again there also Ln provides better results than the nV variants. Interesting also the Rhombicuboctahedron comes with even lower amount of strut lengths than the Icosahedron. The amount of different strut lengths has a direct impact on the construction, the lesser the amount of different strut lengths the better - as you have less cut optimization to calculate and therefore less waste to expect. So it's certainly an aspect to value when choosing a variant to build. As mentioned already, the struts are sorted in 1/10'000th and you may notice on the details of the variants on the following pages, that you can sum together near the same length struts in case you compose a smaller dome, e.g. < 8m or so. For large scale domes it may be crucial to remain as precise as you can and I leave it up to you to treat certain struts of alike length as the same or not. How to Use the Notes I recommend you choose a dome variant you like to construct ... look what base appeals to you most, as a first step disregard any other kind of argument check the amount of different strut types, amount of struts itself - and become aware of the overall overhead (e.g. whether building an edgy 1V or 2V, or a smoother 4V or higher with far more struts) how temporary shall the dome become? e.g. a 4V Icosahedron Dome skeleton with 250 struts I raise as a single person in 4-5 hours the higher the subdivision the more exact you need to work, little difference will distort and weaken the construction ... and once you decided which variant(s) you consider more closely, then ... print out that particular page of the dome variant with your settings - as the notes are subject of change, and may later not be available or available with a different notion make a 10:1 or 20:1 sized model (e.g. 6m full scale dome, create a 0.60m model), it gives you a sense of the overhead, amount of struts, connectors etc think about the kind of strut and its connectors you gonna use, e.g. metal, wood, plastic etc and make tests with the actual material, create a 5-way or 6-way connector construction and test its stability Strut Options & Notion For each dome variant there is a small calculator, to calculate diameter to the different struts, additionally the lhole can be entered. Notion of a dome strut (A vs Alath) & lhole Wooden Strut with Flat Connector Timber based strut, metallic plate as connector, rather cheap with average labour. Wooden Strut with Pipe Hub Pipe Hub Closeup (courtesy by Michal Wielgus) Timber based strut, with a steel pipe as connector, moderately cheap with average labour, prefereable for more lasting constructions. Michal Wielgus who sent me the photo used this hub for a 3V 5/9 icosahedron based geodesic dome, he calculated the holes in the pipe for the 5- and 6-way simply by dpipe π / 5 or 6, which was exact enough he said. For the 4-way connectors on the base require the same calculation as the 6-way, and leaving the two bottom directed connectors empty. To be more precise each hub would require the angles according, A, B, C, etc ... Following photos were kindly shared by Haan from Korea , who made a 2V icosahedron based geodesic dome, with 7m diameter, 11cm diameter steel pipe: Haan's Dome (2v icosa, 7m diameter): 10cm thick wooden struts 2008/04/18 10:02 Haan's Dome (2v icosa, 7m diameter): drilling tool & anchor bolt 2008/04/18 13:53 Haan's Dome (2v icosa, 7m diameter): hub detail with steel pipe 2008/04/18 09:53 Haan's Dome (2v icosa, 7m diameter): hub detail with steel pipe 2008/04/18 09:58 Haan's Dome (2v icosa, 7m diameter): complete setup 2008/04/18 10:07 Pipe/Tube based Strut Steel/aluminium/etc tube or pipe, and ends squeezed, also rather cheap with little labour. This options is very popular using conduits. Desert Domes: Conduit Domes Tips has some useful information on this option. Bamboo Strut Bamboo (different diameters) with soft-pipe as connector, very cheap but increased labour, and only suitable for small domes < 4-5m diameter and lower sub-division frequencies (e.g. 2V, 3V), e.g. for play domes. Cut pointing ends 2007/02/14 12:47 4V Geodesic Dome (6.33m) (Closeup 1) 2007/03/16 16:53 Connector (Closeup) 2007/03/17 11:39 For temporary setups it's obvious to use struts which built-in connectors, e.g. endings which operate as connector. CONBAM.de , german bamboo expert, has special connectors for more stable and large domes, with a large dome construction example. Bending the Strut-Endings Strut Angle αstrut The angle αstrut can be calculated with a bit of trigonometry. α shall be the angle between the tangent (green in the illustration) and the strut: h = √(r2 - lstrut2/4) h = r * cos(γ/2) γ = 2 acos(h/r) = 2 acos(√(r2 - lstrut2/4) / r) α = 90-&beta β = (180-γ)/2 α = 90 - (180-γ)/2 = γ/2 α = αstrut = acos(√(r2 - lstrut2/4) / r) finally α is also the angle to bend the endings αstrut. The following pages with all the variant details provides you for each strut the corresponding αstrut as well. Detailed Calculation of the Faces or Hub/Strut Angles Hub/Strut Angles In case you require the exact angles for the faces, e.g. for a pipe hub or for composing individual faces, according the SSS Theorem , known all 3 sides of a triangle searching the angles, we can calculate all angles: α = acos((B2+C2-A2)/(2 B C)) β = acos((A2+C2-B2)/(2 A C)) γ = acos((A2+B2-C2)/(2 A B)) For now, all the faces are sorted and the angles are given for all variants. I may add later a list of hubs and their angles, but you can sort them your based on the construction maps. Next Page >> Page << Prev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | Next >> Content: Page 1: Table of Content, Changes Page 2: Introduction, Origin of the Geodesic Dome, Geodesize: Triangulate & Normalize, Procedure & Evolution of a Subdividing Triangle ... Page 3: Overview of Variants, Numerical Overview, Amount of Struts vs. Strut Variance, Amount of Struts vs. Strut Types ... Page 4: The Icosahedron, 1V/L1 2/3 Icosahedron Dome, 2V/L2 Icosahedron Dome, 3V 4/9 Icosahedron Dome ... Page 5: 5V 7/15 Icosahedron Dome, 5V 8/15 Icosahedron Dome, 6V Icosahedron Dome, 2V.3V Icosahedron Dome ... Page 6: 7V 10/21 Icosahedron Dome, 7V 11/21 Icosahedron Dome, 8V Icosahedron Dome, L4 Icosahedron Dome ... Page 7: The Octahedron, 1V/L1 Octahedron Dome, 2V/L2 Octahedron Dome, 3V Octahedron Dome Page 8: 4V Octahedron Dome, L3 Octahedron Dome, L3 1/4 Octahedron Dome, L3 5/8 Octahedron Dome Page 9: 5V Octahedron Dome, 6V Octahedron Dome, 2V.3V Octahedron Dome, 3V.2V Octahedron Dome Page 10: 7V Octahedron Dome, 8V Octahedron Dome, L4 Octahedron Dome, L4 7/16 Octahedron Dome, L4 9/16 Octahedron Dome ... Page 11: 9V Octahedron Dome, 3V.3V Octahedron Dome, 10V Octahedron Dome, 2V.5V Octahedron Dome, 2V.5V Octahedron Dome ... Page 12: The Cube, Preparing the Cube, 1V/L1 Cube Dome, 2V/L2 Cube Dome, 3V Cube Dome, 4V Cube Dome, L3 Cube Dome ... Page 13: 5V Cube Dome, 6V Cube Dome, 2V.3V Cube Dome, 3V.2V Cube Dome, 7V Cube Dome Page 14: The Cuboctahedron, Preparing the Cuboctahedron, 1V/L1 Cuboctahedron Dome, 2V/L2 Cuboctahedron Dome ... Page 15: 5V Cuboctahedron Dome, 6V Cuboctahedron Dome, 2V.3V Cuboctahedron Dome, 3V.2V Cuboctahedron Dome ... Page 16: The Truncated Octahedron, Preparing the Truncated Octahedron, 1V/L1 Truncated Octahedron Dome ... Page 17: The Rhombicuboctahedron, Preparing the Rhombicuboctahedron, 1V/L1 3/8 Rhombicuboctahedron Dome ... Page 18: Building Models, 3V 5/9 Icosahedron Model, 2V Icosahedron Model, 4V Icosahedron Model, 2V/L2 Cuboctahedron Model ... Page 19: Real Life Application, Options, Connectors, Separate Functions, Cover, 4/8 Sphere Cover Calculator ... Home   ·   About   ·   Tipi   ·   Yurt   ·   Dome   ·   Features   ·   Gallery Print   ·   Bookmark Creative Commons (CC) BY-SA-NC 2005-2017, developed, designed and written by René K. 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