Changing the length of the edge of the Polyhedron

Question

Hope you're having a great day!

I made another post in regard of how to insert an image onto a face of a Polyhedron. I hope you could help me on this one too!

I want to change the length of the edges of my netimage polyhedron without changing his 3D model. Is it possible?

My polyhedron is:

PolyhedronData["DuerersSolid", "NetImage"]

I want to change its edges. Is it possible?

To clarify, for my own interest: you want to have essentially the base 3D model be modified? But still remain the same? This is pedagogically opposed in my brain, can you explain what you are looking for slightly more? You can most definitely change the length of sides as you wish (I do not know how off-hand) but you would then change the model into a new one? (To my understanding then, the 3D model would be different.) — CA Trevillian, May 21 '19 at 12:49
yeah! The first thing you said! I want to modify the lenght of the edges without changing the actual Polyhedron — Mattia Rugna, May 21 '19 at 12:58

Carl Lange · Answer 1 · 2019-05-21T13:50:54.260

2

Since the "NetImage" property of PolyhedronData is just an Image, you can only ImageResize it:

ImageResize[PolyhedronData["DuerersSolid", "NetImage"], Scaled@2]

This can cause rasterization artefacts and defects, which is probably not what you want.

You may want "Net" instead:

PolyhedronData["DuerersSolid", "Net"]

This outputs a scaleable Graphics object. You can see in the InputForm of this object (InputForm@PolyhedronData["DuerersSolid", "Net"]) that it does not have specific units in mind, and is scaleable. To scale it from the notebook interface, simply click on it and drag the handles. To scale it from code, you can use Show and ImageSize like the following:

Show[PolyhedronData["DuerersSolid", "Net"], ImageSize -> Full]

You can also get other types of output from "Net", including "Graph" and a list of coordinates.

You can also do things such as create a MeshRegion from the Graphics object using DiscretizeGraphics:

It's important to note that these properties ("Net" and "NetImage") are not computed directly from a 3D object - they are pre-computed.

edited May 21 '19 at 13:50

answered May 21 '19 at 13:45

Carl Lange

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Thanks! I want to change the image directly (Moving one edge and twist a triangle, for example), is it possible? – Mattia Rugna May 21 '19 at 13:50
Perhaps, but you may not be able to easily "reassemble" the polyhedron - is this your ultimate goal? – Carl Lange May 21 '19 at 13:51
Yes, it is! Could you please show me how to do it? – Mattia Rugna May 21 '19 at 13:58
Unfortunately, I don't know how you might best do that. Perhaps if you spend some time searching on this site, you might have some luck! – Carl Lange May 21 '19 at 14:36
Thank you anyway! If i found something interesting I'll let you know then!! :) – Mattia Rugna May 21 '19 at 14:38
This might be useful to you. – Carl Lange Jun 04 '19 at 19:12

Changing the length of the edge of the Polyhedron

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