# Strombic Hexecontahedron from a dodecahedron

The purple is what I want, the grey is what I have.

Somebody already helped me on the Blender Discord server, but if you can see, there is no "symmetry", as the pyramid orientation angles are not faced parallel with a dodecahedron.

I have this, but I need to rotate each pyramid with a fixed angle, along each pyramid vertical axis. I can generate an edge between the center of the base of the pyramid, but I need to rotate each pyramid, along each perpendicular axis, according to the same angle.

I'm just looking for the correct procedure.

This can be done via the UI.. it's relatively destructive, but here goes..

• Enable the shipped add-ons Add Mesh : Extra Objects, and Bool Tool
• Set your Pivot to 'Individual Origins', and your Transform Orientation to 'Normal'

• Add a Mesh > Math Function > Regular Solid > Dodecahedron
• ShiftG Select Similar, by Length, unwanted edges, and CtrlX dissolve them.
• Assign, and apply, an Edge Split modifier, to separate all the pentagonal faces

• All selected, Face Menu > Poke Faces.
• Again, using ShiftG, select central vertices, and GZ move them out along their normals.
• Select all the edges at the bases of the pyramids (..ShiftG.. ) and F Fill them all.

• With all selected, you can SZ,GZ, and RZ the pyramids, or just their bases, to their desired positions / heights / rotations, simultaneously.
• When happy, you can P separate the pyramids to their own objects, by loose parts, and..
• .. select them all, with one active, and use Bool Tool's ShiftCtrlNumpad + to make an Auto Union of them all
• If you H hide a few faces, you may see a little dodecahedron inside... :) ...which you can delete :(.

You now have a clean manifold surface , you can bevel, subdivide, etc.

• Thanks, I did it! some details: I did not understand nor seem to need the Edge Split Modifier. For some reason I did not have a center dodecahedron. I did not need to separate them nor union them again... Jul 8 at 21:19
• @jokoon Ahh.. Was I thinking too far ahead? I went for the Edge Split, to make islands, anticipating Individual Origins, which is per-island. do you split the mesh at some later stage? You will only get the baby dodecahedron if the bases of your pyramids intersect around that volume :) The reason for the union is to achieve a watertight, manifold, single surface.. in case you need to print. Jul 8 at 21:27
• @vklidu Dooooooh! 8/ Jul 10 at 18:32

Face instances.

TBH not totally sure I'm on track here, re symmetry of desired result, will go thru the process of adding as dupliface objects, aligned to the face normals

Enable Add Mesh Extras Addon and add the dodecahedron from the presets Add Mesh > Math Functions > Regular Solids

Add a dodecaheron, dissolve the long edges crossing the pentagon

In edit mode select one of the long crossing edges Select > Similar > length and X dissolve edges, leaving only 12 pentagon faces.

Five vert cone as pyramid, have arbitrarily moved origin to base Make it a child of the dodecahedron. (Note all are added at origin)

Note, could do the math, use the measure tool, or use python console to find the "radius" of pentagons.

With dodecahedron as active object, subtracting the location of face center from any of the faces vertex coordinates will be the radius in local space.

>>> me = C.object.data
>>> f = me.polygons[0]
>>> f.vertices[:]
(15, 5, 18, 19, 7)

>>> r = f.center - me.vertices[5].co
>>> r.length
0.607061987083976


Duplifaces

Manual: Instancing Faces

With dodecahedron active, in the instancing properties panel, choose faces.

Fortunately the default alignments match producing a regular. GIF above demonstrates effect of object mode rotation on duplis, and below edit mode. (aka "rotation applied")

Effect of rotating cone, around its local Z axis in edit mode

• Wow, did not expect such thorough answer so fast! I'm going to test this! Thanks! Jul 8 at 11:05
• I don't understand, how did you orient the cones perpendicular to the faces of the dodecahedron? Jul 8 at 12:19
• Duplifaces aligns the instance object to location of face center and local-z axis tracks to face normal. Prob should have explained more, this is why removed edge to have pent faces. The cone is a child of the dodec. Jul 8 at 12:24
• Are you going to explain more? Jul 8 at 13:20
• added manual link re duplifaces. Above demonstrates doing so with dodec and 5 sided cone, to align 12 instances of the cone to each face. Best explanation I can give is to suggest play around with blender. Could you please elaborate on what the target shape is. It looks to me achievable via the rotation on Z in edit mode. (Change cone scale and origin to suit.) Jul 8 at 14:40