# Rhombic Spirallohedron - Script or Poly

More on it here:

http://home.strw.leidenuniv.nl/~snik/html/NTS.htm

and here:

http://www.cutoutfoldup.com/977-rhombic-spirallohedron.php

(from the same source):

and here:

http://library.wolfram.com/infocenter/MathSource/613/

and here:

and here (4 min video)

I’ve tried playing around with modifiers (simple deform / curve modifier), but, haven’t been
able to recreate it.

Since it’s mathematical and perhaps parametric, perhaps there’s a way to script (or formula) or node it
into python or math functions or sverchok (some combination python / nodes).

I’m no mathematician.

Anyone?

Any ideas?

I like spirals but

did not see any algo or equations!
if you find some let us know
and I might be able to make a script !

happy bl

This looks like something that could just as easily be done either way.

It’s the kind of thing that looks like it could be done in sverchok using nodes,
to have looked at some of the examples.

Here, I used a UV sphere. Kept getting tripped up trying to use a cube or a cylinder.

Ten divisions up. Four across. Two subdivides across each section. Ten x Four x Three total.

Simple deform modifier (twist). Scaled across the Z access.

Compare it to the cut and fold.

Looks pretty close.

it’s realy can be made in sverchok. as i see, rotation+scale(by sinus) to matrix and matrix apply, than uvconnect node. and multiply

look at examples and I think you need to keep all quads for this model!

happy bl

Yeah. I noticed that too.

well if you find some algo it might be possible to use it for an addon

happy bl

some stuff i found online on this subject that may be of use -

Quote - “Investigation of the rhombic polar zonohedra led to the discovery of related forms I call “k-armed rhombic spirallohedra.” They have cyclic symmetry, by a k-fold rotation around the symmetry axis, but do not have central symmetry. 3- and 4-armed spirallohedra close-pack to fill space, despite being bounded by thousands or millions of faces.”

http://demonstrations.wolfram.com/RhombicSpirallohedra/

I also found this image after a bit of digging… Maybe some good coders could make use of this? -

I’ve got a raspberry pi.

The nice thing about that is it now comes bundled with Mathematica (for educational use only).

So, I can load an nb, but, doggoned if I can figure out how to use it.

Seems to me, there might be a way to create a spirallohedron via Mathematica and export it to
STL.

But, got to be able to figure it out first.

Mathematica’s got tons of interesting demo projects, but, it looks like there’s also a dividing line
between what’s possible (like Adobe Acrobat) with the Reader vs the Pro (gotta make a buck)
version.

Interesting shape.
This was my approach, select edges separate them, smooth and rebuild the shape again.It takes no time at all.

untitled.blend (619 KB)

I had the idea of copying the image from the Demo project and then tracing it.

Dumb idea. All I got was flat curves.

Yours is much better.

I cleaned up the tops with subdivides, merging of vertices, some insets and some rotations.

Still not nearly as finished as Rambo’s but closer than my first try. All “quads”.

With a little more twisting and tweaking it could be downright presentable.

And using a UV Sphere, the lion’s share is as easy as adjusting the segments, rings and subdivides.

closer_blend.blend (2.96 MB)

I’m still inclined to think there’s a way to create a simple subdivided spiral, using Sverchok’s methodology,
rotate it and skin it and come up with something comparable as well.

Minute he mentioned sin’s, I knew I was out of my depth.

like that may be

mostly done with modifiers

happy bl

### Attachments

What’s the point of the cube in between (in the Blender file)? Is it just a reference or is there some mapping involved to the skeleton spiral?

Duh. Just took another look at it.

Lightbulb.

Nevermind.

Just a short vid.
https://sendvid.com/2d2z60l2

Ok, here’s my version - Rambo’s method.

A lot cleaner, closer to home.

A YouTube video for Rhino (programming):

The document referenced for the formulas used:

https://hal.science/hal-01941511/document

Perhaps it can be done with “extra objects” addon if someone could make the functions

My version… Not Mathematically Correct
Shift+A Mesh > Math Functions > Regular Solid

Select this in the Pop-up Left Bottom…

Subdivide edges 3 or 4 times…

Add a Subdivision Modifier set as you like 2 or 3 divisions…

Add a Simple Deform Modifier select 360, and Z axis

Hi,

Construction ( for 4 “faces”) :

Add - Curve - Curve Spirals - Logarithmic

Convert → Mesh → 25 vert (see pict)
Duplicate → Rotate Z (90°)
Select 7 first verts → Extrude (snap to next vertex),
repeat extrusions to the bottom of the curve (Select all - Merge by distance).
Duplicate the mesh, 3x with a z rotation of 90°.

Adapt the operations for other shapes (3, 5, 6… “faces”).

Good night