Medial Rhombic Triacontahedron (MRT) - Better Edges?

Medial Rhombic Triacontahedron:

When I scaled down the outer vertices, it looked to be created from (or based on) an icosahedron. So, I started there. The one below on the right is mine. The others are from assorted other sources.

My question is, is mine any less a Medial Rhombic Triacontahedron? It’s much more compact and easier to reduce (presentably) to the edges minus the faces. It subdivides well. The others don’t. The edges extend into and beyond. They just look uglier by comparison. As a solid, I suppose. But, in trying to save space, something that is limited to the eseential edges and subdivides accordingly, just seems better constructed (at least for purposes of 3D printing, where cost matters).

Yours seems perfectly reasonable to me. That’s a fun shape!


Thought I’d follow up once I had a handle on my modeling process.

So, here’s the Blend file (sort of a tutorial with the models laid out in progression on the 3rd layer) as
an example, as well as the steps I took in text for reference.

It’s not quite a beginner’s tutorial, but, fairly straightforward, I hope.

If not, let me know.

Layer 1 is my finished product. Layer 3 is for the steps and incremental models.

medial_rhombic_triacontahedron_Tute_blend.blend (547.5 KB)

don’t know if there is like a math way of doing it with a script
could be added to the addon for math shapes

but looking good

happy bl