How to create a non-standard platonic?

[Jim Scott]

In order for it to be spherical there needs to be more polygons. To achieve a spherical shape with polygons of approximately equal size, and an “outside” edge (or perimeter) that has 10 sides when viewed from the proper angle, create an icosahedron sphere with 11 segments, turn off “Render Perfect,” and delete the phong tag. Below is an image of just such a sphere viewed from two angles. I created sweeps for all the polygon edges for better visibility, and made the one showing the perimeter slightly larger and red in color. Hope this helps.

[Scyld]

many thanks jim. any idea how to edit the individual vertices so it looks like the 2D artwork? how to get those wavy lines?

[Jim Scott]

Hi Sean,

I wasn’t sure if you were trying to recreate the entire drawing as a 3D object or just create a sphere with the 10 edges. So are you trying to end up with what amounts to a flat panel (like the image below but with triangular segments and wavy lines), or something else… like a hemisphere with wavy pipes (a children’s jungle-gym in the shape of a dome comes to mind)?

[Scyld]

the latter i’m afraid. they want a non-transparent hemisphere. i figured i could edit an existing platonic to mirror the 2D diagram i was given, but my modelling skills are basic at best. i was thinking to have it rotating and the final resting frame matches their 2D pic. what do you think? is this 10 sided polygon even mathematically possible? can you help?

[Jim Scott]

Like you, my modeling skills are not my strong point as I mostly play around with mograph-type projects. And the mathematical possibilities of 3D objects is beyond my brain power. As my example showed, getting a spherical object with the desired 10-sided perimeter is definitely doable, but for it to be anything near symmetrical (and with equal-sized polygons) simply requires more polygons. I imagine that it is possible to recreate the drawing in C4D by connecting points but that’s not something I’ve ever done. And turning it into a dome shape would require that the fewer polygons are highly stretched and asymmetrical. I’ll keep playing around, though, and let you know if I come up with anything. Sorry that I can’t be of more help, and hopefully a more experienced modeller will chime in. Good luck.

[Brian Jones]

not easy to get a sphere shape with that geometry division here’s my try

13153_nonstandardplatonictrial.c4d.zip

and a link to the closest platonic https://en.wikipedia.org/wiki/Regular_dodecahedron
– has 10 sides when viewed from the front etc…

[Jim Scott]

Good work Brian. What were the steps you took to create that platonic?

Thanks

[Scyld]

many thanks brian! do you think it is mathematically impossible to get all facets the same triangle size?

[Scyld]

also my bad on describing the goal polygon as a hemisphere. that should be sphere.

[Brian Jones]

the basics were
-working from the Top view to match the drawing
-making a 10 sided n-Side spline
-using the spline Pen tool to draw out the filling/crossing lines
-cutting the splines where necessary to have vertices for the next step
-added a polygon object, deleted the simple poly that gets created and used the Polygon Pen with vertex snapping on to make the flat version of the object
-use Move tool in points mode with Soft Selection on with Falloff set to Dome and Mode set to Center so it pulls the points up in a spherical shape

Spline.7 isn’t really needed it was just an experiment, the x-ray sphere is just to try and hit a spherical shape when pulling up with the Move tool.
While a spherical shape is not reasonably possible with that construction a small lift of the center of the polygon object looks ok, depends on what Sean’s clients are really after