Is it a helix or a trihedron?

I submit a very particular imported file which has precisely proportioned separations of edges and vertices, (although the overall size is irrelevant).

I kindly ask if there is a “faceted” or a “straight-sectioned-step” version of the Rhino7 helix. The attached object was a generated helix, wound around a much smaller equilateral triangle. Its native app offers an old fashioned parametric option of facetted or smooth output, (in its helix tool that has not changed to my recollection in over 25 years).

I have a longstanding interest in this very particular kind of object which is generated by one click, by winding a helix around a much smaller equilateral-triangular path; and initially setting the number of steps to 9 total, and the radius of the helix, (with each step as a straight line segment, as 9 divisions total).

A near likeness to a tetrahedron or trihedron is formed, which is a bit surprising for a helix tool to generate in one step, and therefore I’m curious if Rhino7 does facetted helixes, for me to verify the nature of this seeming generation of a polyhedron, and what mathematically causes the cyclic peaks to converge towards a vertex, but as a convergence, it does not quite make a closed vertex.

Insights would be much appreciated.
100to1-faceted-trihedron.3dm (1.8 MB)

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Helix command with desired diameter, pitch/number of turns, etc to create helix

Rebuild to degree 1 with desired number of facets.

HelixFacetsDC01.3dm (1.6 MB)

For a “helix” around a curve use the Spiral command. Rebuild to degree 1 can be used to convert the spiral/helix to a faceted curve.

Please, where is the rebuild function on a Mac? I do see the other options as appear on the left-side tool area, when the helix around path is made, but the word rebuild or facetted are not yet seen.

You will not find the word “facetted”. I’m not a Mac user but I did find this on Rhino 7 for Mac Help:

Rebuild is a fundamental Rhino command.

I found Rebuild in the edit menu, selected it, and clicked on the smooth helix and got the 1 degree setting, but the outcome was very unsymmetrical…

I used the Rebuild command on the smooth helix which Rhino generated, based on a the equilateral triangle of the small size at 0.0.0.)

My attached file was supposed to have a small triangle which the import edited with inscribed parts, so I simply made a copy with the polygon tool: “center inscribed polygon NumSides=3”

So far I have a lot to learn as a beginner of Rhino.

Good places to start learning:
Users Guide
Level 1 Manual
Level 2 Manual

Do not assume Rhino works like other software.

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just to be sure that this was mentioned, if you start typing the command name, they should appear in the command list on your left, commands in rhino are if familiar usually typed rather than selected in the menu.

Mac interface is different than the Windows interface.

I know users of Rhino for Windows who avoid typing commands and use icons or menus if possible.

not universally if we are talking about platform differences regarding Rhino. the main principles are the same, Mac Rhino is a bit more rigid in its UI still, which is supposed to be changed to the better (as i hope) at least it is being worked on for the upcoming version and the document options are layed out different, other than that they work pretty much the same.

One other thing, your big tetrahedron is wildly inaccurate… the vertices don’t meet. For example each top vertex is 0.017m away from its neighbor.

This is also far too small of an absolute tolerance for working in Rhino:
That means you are trying to measure micron tolerances with a meter stick.

Try to keep the tolerances between 0.001 and 0.0001 units. If need be, change the unit system, for an object of this size (~1m) I might work in mm.

It’s not clear to me from the file you posted what your end goal is - can you post an image?

Thanks for the tolerance setting issue, which I just now looked for; however by typing ‘tolerance’ in the Mac/Menu/Help, I could not find the panel you show, nor did I see it in Menu/Rhino7/Preferences. (Also am updating Rhino in mean time.)

After sleeping on it last night, I again found my way through Rhino7 tools on Mac, to generate and Rebuild a new object as: a 9 point count with 1 degree.

Again the Rhino attempt in Mac: ToolPanel/Helix/ Around Curve/ makes an unsymmetrical resultant curve, which might be due to the unacceptability of using an equilateral triangle when prompted by the Helix Tool to select a ‘curve’.

Images here are of direct Rhino generation, while my first 3dm above was an import.

As to the “big tetrahedron”, it is actually very specifically constructed, seemingly as a mathematical convergence which is variable, based on the ratio of the source radius to the tetrahedral-helix-radius. (This function is what I am searching for, now that I can buy into other software like Rhino).

I do realize it is an unusual object which looks poorly made. The larger the ratio of the big object radius, to the small source object radius, (tiny triangle), the closer the vertex closes up.

I have tried ratios of up to 10 million or so, but am not sure commercial software is happy with ever larger ratios.

Thanks for the screenshot of Tolerance listing, which on Mac turned up under Menu/Settings…/Annotated Styles/Toleran…
The strictest settings were wanted and I assume this screen shot shows appropriate settings.

Next I repeated the steps described in my first images above, where Rhino7 generated the helixes, the center object and the object on the right side.

I very much appreciate the key words to search for, to get the best options . So far it appears that Rhino requires smooth curves for the helix/Around Curve tool. Editing via Rebuild is forced to use the unsymmetrical product of all attempts so far.

I attach the current file. Again, the white, facetted tetrahedral helix is the original import.
100to1-faceted-trihedronWednesdayAftn.3dm (3.9 MB)

If there is any other thing to try, please advise.

That is not the tolerance of interest. You need to appropriately set the “absolute tolerance” which can be found in “Units”.
Appropriate settings for absolute tolerance are between 0.01 and 0.0001 with 0.001 probably the most commonly used. Using tighter tolerances such as 0.000001 is likely to cause difficulties with no benefit.

Please take time to read through the User’s Guide. Rhino - Learn to use Rhino

Do not use “Make SubD Friendly” or “SubD Friendly” or similar options anywhere.

The white polycurve sort-of tetrahedron has different length sides.

It is not obvious what you are trying to do.

Thanks for your patience, and I will continue to scan though Rhino links with care to find the key words discussed in this thread. The guides are masterfully put together, however the key to all human endeavors is our personal drives, and in this case mine is to locate the full range of Rhino7 helix options for faceted helixes or helices.

Indeed, the facetted form of a helix can be manually and arbitrarily mocked up but this one is not arbitrarily mocked up. The white, imported, trihedral or tetrahedral-helix is of unequal edges because it is a convergence implying it is of a lower rationed radius, of around 100 to 1, as compared with higher ratios, to arrive at closer-to-equalized-edge-lengths.

My search is for affordable tools which can dial up higher ratios of radii, higher than was possible with my humbler software used up to now. This was one reason I invested in Rhino.

With all the highest of respect may I add, and understandably so, Rhino developers were not tasked to prioritize this unpopular area of 3d modeling, and I am not aware of any software which would prioritize facetted helices, and handle ratios up into the highest limits possible, and with two radii involved, due to winding around a faceted, (equilateral) triangle.

I assume the Helix/Around Curve tool makes the unsymmetrical windings by clicking on the tiny equilateral triangle which I drew in Rhino, (zoom way into the center of the central object, and find the 100 times smaller triangle).

Or generate one’s own tiny triangle and wind a helix around that with a 100 times larger radius. The sharpness of facetted ‘curves’ throws the helix tool off from regularity of symmetry, and my effort in this post is simply to see if this is “as expected”. Even a 24 edge, polyhedron, in the old days an acceptable circle, throws off the outcome of symmetry, whereas smooth curves produce the cool sort of products in demand by stylish designers.

are you trying to geometrically construct a mathematical problem or what are you aiming for?

it’s a little bit of everything, to cross examine why and how 3d softwares draw helixes, spirals and curves, but especially how one software offers the option of smooth versus facetted versions, and amazingly drew the tetrahedral-trihedral object as a helix… does that make sense?