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Polyhedral dice & platonic solids 2D CAD

Design interlocking shapes for assembly of a dice set or platonic solids

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I wanted to make some big dice for amusement and ornamental purposes rather than actual gameplay. With having access to a laser cutter I took a 2D CAD approach and designed the faces of each shape. Initially the intent was to design a parametric model using OpenSCAD, however, after much thought I ended up using LibreCAD instead.

All of the platonic solids are simple to make from tessellating faces. Dice such as a D4, D8 & D20 all use the same triangular faces which for the most part are interchangeable. A D12 is also a simple platonic solid which uses pentagons for each face. However, a D10 is very different. Not only because there is no standard for its shape, but due to angles the faces are difficult to assemble.

To simplify dimensions each face has initially been designed with 40mm long edges, having 4 tabs of 5mm width and 3mm depth. This decision means that all shapes were easy to create with the caveat of not paying attention to relative scales. For example the D12 is huge due to it having numerous polygonal faces instead of triangular. The other polyhedral dice or platonic solids seem to scale more aesthetically. A 3mm tab depth is chosen because 2.8mm poplar ply is at hand, inexpensive, and great for laser cutting.

Since the initial success of assembling several dice shapes I have decided to increase the positive tab width to 5.2mm. This allows for a tight fit once laser cut.

When engraving wooden dice I prefer to defocus the laser and run a vector instead of raster. This can make the operation much faster and cleaner than rasterising solid characters.

For mirror acrylic it is best to cut from the back (reflective side down) and rasterising with a mirror image. This is also generally a good approach when using regular acrylic.

D4-faces-numbered.dxf

Numbered triangular faces for constructing a D4 tetrahedron

AutoCAD DXF - 36.02 kB - 09/28/2021 at 14:08

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D8-D20-faces-numbered.dxf

Numbered triangular faces for constructing a D8 octahedron or D20 icosahedron

AutoCAD DXF - 73.01 kB - 09/28/2021 at 13:29

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D12-pentagon-face.dxf

Pentagon face for constructing a D12 dodecahedron

AutoCAD DXF - 32.30 kB - 03/10/2021 at 12:11

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D6-square-face.dxf

Square face for constructing a D6 cube

AutoCAD DXF - 27.03 kB - 03/10/2021 at 12:06

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  • 1 × 2.8mm poplar ply Inexpensive and great for later cutting
  • 1 × C.A. super glue Medium viscosity works best for flowing glue into joints. Gel is good for assembling final pieces which can not be reached from the inside. Thin glue should be avoided as it will flow too far and stain the workpiece.

  • RPG Dice set relative size

    Sproket10/01/2021 at 08:09 0 comments

    I have a generic cheap set of plastic RPG dice which I hope to use as a reference for my larger laser cut versions. The plan is to quantify some form of relative scaling/size.
     

    Dice measurements in mm to one decimal place
    
    Dice | Edge length | Height | Height % (Based on D20)
    -----|-------------|--------|---------
    D4   |     20.2    |  17    | 85
    D6   |     16.2    |  16.2  | 81
    D8   |     18.8    |  15.9  | 79.5
    D10  |  15.9  7.2  |  15.9  | 79.5
    D12  |     8.2     |  17.9  | 89.5
    D20  |     12      |  20    | 100
    

     
    The D20 is 20mm tall <3

  • D10 dice are /complicated/

    Sproket04/28/2021 at 11:10 0 comments

    The shape of a D10 die has no standard, it is not a platonic solid, and none of the angles are regular.

    Using a Stack Exchange post on the subject as inspiration (https://rpg.stackexchange.com/questions/114672/is-there-a-standard-d10-dimension-ratio) I designed D10 faces based on a regular kite with two 90' angles. It worked but was not aesthetically pleasing. The shape was short and wide, similar to a spinning top.

    So then after watching a well timed video from Wesley Treat (https://youtu.be/OEdxLarEGTE Welding Giant Polyhedral Dice) where he suggested using 66.6' as two angles of a kite. It didn't seem to work for me and assembling the D10 was even harder than the 90' regular kite faces. Have a hunch where I went wrong with the angles though.

    Skip to now with finding a very well implemented dice generator on github using OpenScad (https://github.com/charmaur/PolyDiceGenerator PolyDiceGenerator). I chose to render a D10 and implemented projection(cut=true){} in the code to take a slice which was then exported as DXF. I resized the long sides in LibreCAD to 40mm and added my usual tabs for finger jointing the shape. We shall see.

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