DRAWING AN ICOSAHEDRON OR TETRAHEDRON SHAPE

[tallboy]

What is the best method of drawing an truncated icosahedron (essentially a soccerball shape), or tetrahedron, dodecahedron, or other such complex shapes in Vectorworks.

i'm running vectorworks 12.5 on a mac powerbook

not sure how to approach these shapes -

Edited February 25, 2009 by tim joyce

[Chad McNeely]

Tetrahedron is easy, just a 3-sided regular polygon, a 2d locus at its center, and multiple extrude where the height is about .816 [or (2/3)^.5] of one of the triangle's sides.

Icosahedron is a bit trickier, and would likely involve folding up 3d triangles and adding them together. I recall going through this a few years back with a soccer ball (which is a truncated icosahedron) challenge.

Ah, found it. Soccer ball file attached.

[tallboy]

thanks,

will check the file, and may have other questions,

cheers.

tj

[Chad McNeely]

Ooops, just saw your VW12.5 note. Here's a VW11 version of the soccer ball.

[islandmon]

Programming geodesics is fun & simple once you know the primary shape, rotations, dihedral angle(s) , and reflections.

__________

For example, tetrahedron = 60? tri, 3@120? rotation, 70.5288? dihedral, central angle = 109.4712?.

1) Create 3d= 60?TriA with side=1 @ 000 pointing in the Y direction , then create TriB by a reflection of A along the base.

Goto the rightside view and rotate TriB at the baseline by 109.4712? to apex alignment with central Z axis at a loci height of 0.816496=sin(90-35.26438)=height of tetra .

Goto Topview and dup&rotate B by 2@120? to create C & D.

___________

The dodecadron = pentagon, 5@72? rotation, dihedral = 70.5288? & 109.4712?, central angle = 50.4666?

[Kjonz58]

On 2/25/2009 at 4:45 PM, Chad McNeely said:

Tetrahedron is easy, just a 3-sided regular polygon, a 2d locus at its center, and multiple extrude where the height is about .816 [or (2/3)^.5] of one of the triangle's sides.

Icosahedron is a bit trickier, and would likely involve folding up 3d triangles and adding them together. I recall going through this a few years back with a soccer ball (which is a truncated icosahedron) challenge.

Ah, found it. Soccer ball file attached.

Please share!!! I am going crazy trying to find or create a soccer ball 3D texture!

[Benson Shaw]

OK, here's the 1st installment.  The flat faced version.  Main trick is to establish the fold angle of the first ring.

See also this:

 

The inflated version is a somewhat more elaborate process. Will include the file. Coming soon.

 

 

-B

 

 

 

 

 

Edited October 8, 2022 by Benson Shaw
Splitting hairs

[Benson Shaw]

Here is the soccer ball inflated. Similar process, but added steps and options.

v2023 file included.

-B

 

 

 

 

 

 

 

 

 

 

 

 

Icosahedron.vwx

[Kevin McAllister]

Amazing tutorial @Benson Shaw!!

Wouldn't it be great to have a rotate tool that didn't need the guide plane 😊

Kevin

[Benson Shaw]

@Kevin McAllister Yes, that would be great.  These rotations and other "off plane" operations can trip me up. So I revert to guide objects, knowing that they will work.  I think there are multiple ways to accomplish, but they don't always come to mind.

 

For bonus points on the soccer ball, edit the symbols - shell to the concave side for a little thickness.  Fillet the outer edges to make the seams recessed.  If building another ball, probably means hiding the round classes and working with the flat versions to access the vertices.

 

-B

 

Edited October 9, 2022 by Benson Shaw
Lost in the void

[thedopepope]

Coming back to this several years later im trying to do the same thing, but I'm having trouble getting the exact fold angle any tchniques or tips? 

[Benson Shaw]

Soccer ball? or icosahedron? or?

 

Do it by the geometry.  Knowing the exact angle value is not needed. Use guide objects - loci, lines, arcs, planes.  That 1st fold between  pentagon and hexagon is the key. In this image copied from above, the big pink pentagon has edge length equal to the hexagon diameter (or if making icosahedron, fold is between 2 pentagons. Use the pentagon width for edge length of larger pink pentagon).

 

 Use the Regular Polygon tool in the Basic tool set. Set to 5 sides and edge mode. Click click across the hexagon (makes the guide pentagon).  Center the new guide pentagon on the original pentagon.

 

Rotate tool operates on that guide plane. Rotation (fold angle) is determined not by entering a value, but rather by snaps from start of the guide arc to end of the guide arc.

 

-B

 

 

[bcd]

This is a coder's dream.

Just build a new Platonic Shape tool to incorporate any number of these.

 

@Benson Shaw still up to his tricks!

 

[Benson Shaw]

Wow! They take the edit away early.  That shape with all pentagons is Dodecahedron, not Icosahedron. My bad (also didn't do well in Latin)

-B.

[VIRTUALENVIRONS]

@Benson Shaw

Amazing work Benson.  Travelling this week, just saw this on Iphone.  Wonderful.