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The rhombic triacontahedron is an Archimedean solid, which consists of 30 Rhombuses

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I need a model like this to be a base for one of my projects.

I thought about creating a solid with 10 hexagons as base and then subdivide it, but I couldn't manage it at the end.

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2 Answers 2

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This shape can be modeled using Extra Objects addon or in a manual way.

Extra Objects addon has preset accessible for rhombic triacontahedron. You'll need to activate addon in User Preferences, see more on how to activate / install an addon.

With addon enabled, from Shift+A menu find Mesh > Math function > Regular Solid. Then you'll tweak its parameters:

scr of adding mesh

In Last Operator panel load preset:

scr of setting up mesh

Or change parameters for Source, Vertex Truncation and Dual.

To model it manually:

  1. Start with icosphere, 1 subdivision.
  2. Poke faces with Alt+P.. This will create geometry necessary for the middle of rombes.
  3. Select one newly created vertex (from poked ones).
  4. Select similar with Shift+G > Amount of connecting edges. Scale them out along normals a bit.
  5. Select all, convert to quads (Alt+J).

GIF modeling mesh

  1. As resulting faces are non-planar (i.e. not all vertices are located on the same imaginary plane), make them planar using Mesh > Clean-Up > Make Planar Faces with around 4 iterations (thanks to Leon Cheung).
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  • $\begingroup$ well : ) ... I was close : )) $\endgroup$
    – lemon
    Commented Jul 25, 2016 at 16:54
  • $\begingroup$ For the manual method, actually you can hardly scale to make all quads planar enough in this way. I would suggest Alt J then increase the Max Face Angle parameter, then Mesh > Clean Up > Make Planar Faces, increase the Interations. $\endgroup$
    – Leon Cheung
    Commented Jul 26, 2016 at 4:15
  • $\begingroup$ @LeonCheung you are right, they are non-planar. I thought about that but for some reason didn't check. Generally, it's still possible to scale those vertices - Make Non-planar will handle with the job, so there won't be non-planar ones under 5 degrees. $\endgroup$
    – Mr Zak
    Commented Jul 26, 2016 at 9:20
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You can start from a dodecahedron to do that.

enter image description here

The dodecahedron is a regular solid given in the 'extra object' addon. It looks like this:

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So, starting from it, the idea is to remove each edge which cut each pentagon (do that for all the pentagons):

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And replace it by a center, like this:

  • Extrude E, then scale to zero S0

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Once done for all faces, you can remove all double and obtain this which is the geometry you want, except that rhombic parts are not flat:

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To make them flat, select all the pentagons centers, then scale:

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This scaling will be approximative, but now:

Enter edit mode again, select all, then make quad with AltJ:

enter image description here

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  • $\begingroup$ For the first step, you needn't do that for all pentagons, just select all then X -> Limited Dissolve. Another way is selecting one of the diagonale then Shift G > Length, then X > Only Edges & Faces, then select all and F to fill all holes with ngons. $\endgroup$
    – Leon Cheung
    Commented Jul 26, 2016 at 4:28

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