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How to draw a spherical polyhedron or Geodesic Dome
Read 689 times
* May 28, 2017, 11:54:08 AM
Hi,

Best way to describe what I want to draw is a soccer ball. I want it with flat sides not radius sides. Like tiling the soccer ball with polygons and pentagons. I would like to be able to do it in 2d as I am not very well versed in 3d. Have not had a need for 3d since all my shop drawings need to be in 2d for prints and CNC machines.
I am using TC Pro Platinum 21.2.
 
Thanks,

Doug

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* May 28, 2017, 02:55:56 PM
#1

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John R.

V17—V21, 2015, 2016, 2017
Designer, Deluxe, Basic, Platinum
RedSDK enabled
Windows 10, 64-bit


* May 28, 2017, 03:13:37 PM
#2
John,

I had already seen that in a search prior to my posting. It does not explain how to set the size of the polygon & pentagon in relation to size of the ball (sphere) and it was all hand drawn. What I did find on the search was all hand drawn examples that did not explain the above. Was sort of hoping to find someone that had already done a drawing like this.


Thanks,

Doug

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* May 28, 2017, 04:00:01 PM
#3
Maybe this will work.
  • Activate the "Polygon" tool.
  • use 6 Sides, 0 Angle, Side length @1" & Vertex mode.
  • Lock the Side Length (Ctrl+L)
  • Draw the polygon.
  • Activate the "Edge" option.
  • "V" snap the edges of the polygon, left to right.
  • Work your way around the base polygon.

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John R.

V17—V21, 2015, 2016, 2017
Designer, Deluxe, Basic, Platinum
RedSDK enabled
Windows 10, 64-bit


* May 28, 2017, 04:13:46 PM
#4
My question Doug would be, since you want to draw it in 2D:
Are you wanting a 2D representation of a face-on or other orthographical viewpoint;
or are you wanting a 2D representation of the thing unfolded?

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Alvin Gregorio
(mostly Residential Architectural 2D; no formal CAD Training; intermittent TurboCAD user since yr. 2000 [ver6.5])
---TurboCAD: V20.2PP(57.0)[as of 3/12/15]; V19DL(54.2); V11.2Pro; Windows-7-Pro/64-bit; Intel-Core-i3 CPU; 2.27ghz; 4GB RAM; Intel HD Graphics (CPU based)


* May 28, 2017, 05:13:11 PM
#5
Best way to describe what I want to draw is a soccer ball. I want it with flat sides not radius sides

One of these  - https://en.wikipedia.org/wiki/Truncated_icosahedron

Just had a play, and the problem for me is knowing the required initial (centre pentagon) edge length required, it would need maths to find this for a given sphere - not my strong point.
« Last Edit: May 28, 2017, 06:53:33 PM by Andy H »

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* May 28, 2017, 07:26:17 PM
#6
Here's a 3D polyhedral "soccer ball." Maybe you can make the required 2D views from this.

Henry H

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* May 28, 2017, 08:00:43 PM
#7
Here's a 3D polyhedral "soccer ball." Maybe you can make the required 2D views from this.

Henry H

How did you make that Henry?  Did you use math, geometry, and other knowledge stuff to enter the correct required angles?

I've been messing with it for hours before you posted (I'm bored, as usual on a Sunday), and I just couldn't figure out how much to rotate the hexagons.

-Alvin

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Alvin Gregorio
(mostly Residential Architectural 2D; no formal CAD Training; intermittent TurboCAD user since yr. 2000 [ver6.5])
---TurboCAD: V20.2PP(57.0)[as of 3/12/15]; V19DL(54.2); V11.2Pro; Windows-7-Pro/64-bit; Intel-Core-i3 CPU; 2.27ghz; 4GB RAM; Intel HD Graphics (CPU based)


* May 29, 2017, 03:52:54 AM
#8
Someone  did something very similar in 3d before. I was curious and I found a site with those "magic angles" forgot the real term for the angle. Pentagonal diacahedron - 63.435 degrees.
Soccer ball - 37.377368 degrees
Hexagon with surrounding Pentagons - 55.75191
Tetrahedron - 109.47
Pyramid - 125.26

There is a video tutorial for a 3d soccer ball for AutoCAD. I watched that and was able to recreate it in turbocad

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Nikki
TC20 platinum
TC 2015 platinum
TC 2017 with lightworks


* May 29, 2017, 05:18:44 AM
#9
Hi,

Thanks for all the input.

Nikkipollard I also found the AutoCad tutorial but since I am not doing 3d I did not follow it to well.

Henry there is no a file attached to your response on my view but I see that Alvin had a file to view.
Can you resend the file?

John I'll try what you sent.

Thanks,

Doug



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* May 29, 2017, 05:20:16 AM
#10
Henry,

The file showed itself after a refresh of the screen.

Thanks

Doug

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* May 29, 2017, 06:23:38 AM
#11
How did you make that Henry?  Did you use math, geometry, and other knowledge stuff to enter the correct required angles?

Don't know about Henry, but here is an old soccer ball tutorial by Winston Mitchel from the old forum,   unfortunately some of the 3d bits are missing but its can still be followed (I didn't bother with the using a sphere to get it spherical)

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* May 29, 2017, 07:39:50 AM
#12
How can we calculate the length of the sides in the first Pentagon that later will be the base for Hexagon's so the ball can have a given diameter.
A normal football should have 220-230 mm diameter.

Torfinn

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V18, V19, V20, V21, 2015 Pro. Platinum
Deluxe V20, V21, 2015
RedSDK enabled
Windows 10 Home Premium 64 bit, 32 GB
NVIDIA Geforce GTX 780m, 1 GB


* May 29, 2017, 07:41:03 AM
#13
Here's a 3D polyhedral "soccer ball." Maybe you can make the required 2D views from this.

Henry H

How did you make that Henry?  Did you use math, geometry, and other knowledge stuff to enter the correct required angles?

I've been messing with it for hours before you posted (I'm bored, as usual on a Sunday), and I just couldn't figure out how much to rotate the hexagons.

-Alvin

Started out with a hexagon to which I attached three pentagons and three other hexagons, each figure having equal side lengths. Used geometry to rotate the satellite polygons.  Math would have been easier, but I didn't trust Genie to do it precisely enough. (Actually, I didn't rotate the existing objects; I make copies and "Assembled" them in the new positions 'cuz I thought it might be a little more certain.) Converted each polygon into a "Surface," grouped these seven objects, then made copies and assembled them (which resulted in many instances of two or more polygons in the same place). Exploded all the Groups and deleted the redundant objects. 3D-Added the survivors to make a single object. Finally -- and arbitrarily -- I converted this hollow shell into a "Solid."

Henry H

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* May 29, 2017, 08:08:33 AM
#14
How did you make that Henry?  Did you use math, geometry, and other knowledge stuff to enter the correct required angles?

Don't know about Henry, but here is an old soccer ball tutorial by Winston Mitchel from the old forum,   unfortunately some of the 3d bits are missing but its can still be followed (I didn't bother with the using a sphere to get it spherical)

Thanks Andy-- and Winston-- for posting the tutorial.
Starting at about Step-7, some entities are missing, and the "Hexagon" and "Pentagon" Blocks are empty.  But reading through the instructions, I'm able to follow along well enough.
« Last Edit: May 29, 2017, 10:02:29 AM by Alvin Gregorio »

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Alvin Gregorio
(mostly Residential Architectural 2D; no formal CAD Training; intermittent TurboCAD user since yr. 2000 [ver6.5])
---TurboCAD: V20.2PP(57.0)[as of 3/12/15]; V19DL(54.2); V11.2Pro; Windows-7-Pro/64-bit; Intel-Core-i3 CPU; 2.27ghz; 4GB RAM; Intel HD Graphics (CPU based)


* May 29, 2017, 09:58:15 AM
#15
Started out with a hexagon to which I attached three pentagons and three other hexagons, each figure having equal side lengths. Used geometry to rotate the satellite polygons.  Math would have been easier, but I didn't trust Genie to do it precisely enough. (Actually, I didn't rotate the existing objects; I make copies and "Assembled" them in the new positions 'cuz I thought it might be a little more certain.) Converted each polygon into a "Surface," grouped these seven objects, then made copies and assembled them (which resulted in many instances of two or more polygons in the same place). Exploded all the Groups and deleted the redundant objects. 3D-Added the survivors to make a single object. Finally -- and arbitrarily -- I converted this hollow shell into a "Solid."

Henry H

Thanks Henry.  I ended up being able to do it using a combination of tips from Winston's tutorial and your suggested use of the Assemble Tools.
________
Still wondering Doug, since you stated that you want to draw it in 2D:
Are you wanting a 2D representation of a face-on or other orthographical viewpoint;
or
Are you wanting a 2D representation of the thing unfolded?

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Alvin Gregorio
(mostly Residential Architectural 2D; no formal CAD Training; intermittent TurboCAD user since yr. 2000 [ver6.5])
---TurboCAD: V20.2PP(57.0)[as of 3/12/15]; V19DL(54.2); V11.2Pro; Windows-7-Pro/64-bit; Intel-Core-i3 CPU; 2.27ghz; 4GB RAM; Intel HD Graphics (CPU based)


* May 29, 2017, 12:45:49 PM
#16
Alvin,

I'm needing the polygon and pentagon to be 2d as I am wanting to cut out with cnc. I am just trying to see how to draw it so that when I have a known sphere size I will be able to draw the polygon and pentagon or vice versa. Wish I was better at 3d maybe could understand more of what is going on. I understand basics in 3d since I don't need it to draw shop prints. Have been using 2d software since 1989 and have been using TurbCad since v.10.

Thanks,

Doug

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* May 29, 2017, 12:56:34 PM
#17
I suppose something like below would work(?)
Pretty easy to replicate, once the edge lengths are determined for your desired "sphere" radius.
You could use an online truncated icosahedron calculator to determine the edge length.

Despite the name of the file, I did the below simply by using 2D entities.
« Last Edit: May 29, 2017, 01:16:15 PM by Alvin Gregorio »

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Alvin Gregorio
(mostly Residential Architectural 2D; no formal CAD Training; intermittent TurboCAD user since yr. 2000 [ver6.5])
---TurboCAD: V20.2PP(57.0)[as of 3/12/15]; V19DL(54.2); V11.2Pro; Windows-7-Pro/64-bit; Intel-Core-i3 CPU; 2.27ghz; 4GB RAM; Intel HD Graphics (CPU based)


* May 29, 2017, 02:15:00 PM
#18
Alvin,

Thanks for the link to the calculator. I had looked for one but did not find this one and I think it will work very well for me.

Did you draw out the Png file in TC?

Thanks,

Doug

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* May 29, 2017, 02:29:58 PM
#19
...
Did you draw out the Png file in TC?
Thanks,
Doug

Yes, I drew what you see in the "SoccerBallUnfold-1.PNG" image in TurboCAD.
Extremely easy.
It was based on an image I saw on the Internet, and learning that a "soccer ball" (truncated icosahedron) has 12 pentagons and 20 hexagons, all with equal length sides.

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Alvin Gregorio
(mostly Residential Architectural 2D; no formal CAD Training; intermittent TurboCAD user since yr. 2000 [ver6.5])
---TurboCAD: V20.2PP(57.0)[as of 3/12/15]; V19DL(54.2); V11.2Pro; Windows-7-Pro/64-bit; Intel-Core-i3 CPU; 2.27ghz; 4GB RAM; Intel HD Graphics (CPU based)


* May 29, 2017, 03:51:24 PM
#20
I suppose something like below would work(?)
Pretty easy to replicate, once the edge lengths are determined for your desired "sphere" radius.
You could use an online truncated icosahedron calculator to determine the edge length.

Despite the name of the file, I did the below simply by using 2D entities.

That's a mind-bender, Alvin. Does it really fold into a "soccer ball"?

Henry H

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* May 29, 2017, 04:14:12 PM
#21
I suppose something like below would work(?)
Pretty easy to replicate, once the edge lengths are determined for your desired "sphere" radius.
You could use an online truncated icosahedron calculator to determine the edge length.

Despite the name of the file, I did the below simply by using 2D entities.

That's a mind-bender, Alvin. Does it really fold into a "soccer ball"?

Henry H

Yep.  The two black pentagons that are sticking out on their own at the top and the bottom are the top and bottom of the soccer ball.

I've been obsessed with this soccer ball thing the past two days (my days off).  My truck's broke down, so I can't go anywhere.
One of the first things I came across on the Internet yesterday, when trying to get some conceptual understanding, was this

from this website.
(how'd they do that???)

Folding it in TurboCAD is a pain-- compared to our method of using the Copy and Assemble Tools.  I can do it now, using 2D polygons to create the 3D-looking ball, in under 15 minutes, using the Copy and Assemble Tools, including >Surface from Profile; >3D Boolean MultiADD; >then Solid from Surface.
« Last Edit: May 29, 2017, 04:27:12 PM by Alvin Gregorio »

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Alvin Gregorio
(mostly Residential Architectural 2D; no formal CAD Training; intermittent TurboCAD user since yr. 2000 [ver6.5])
---TurboCAD: V20.2PP(57.0)[as of 3/12/15]; V19DL(54.2); V11.2Pro; Windows-7-Pro/64-bit; Intel-Core-i3 CPU; 2.27ghz; 4GB RAM; Intel HD Graphics (CPU based)


* May 29, 2017, 04:29:16 PM
#22
Alvin,

I did not think anybody would be that interested in what I was trying to do. I did not mean for anybody to obsessed with a stupid soccer ball. I did not know what to think of the level to which it would take to do this.

Thanks,

Doug

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* May 29, 2017, 05:01:53 PM
#23
Alvin, that's fantastic.

Henry H

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June 01, 2017, 08:11:49 AM
#24
Hi I remember bending my mind inside out learning how to draw the soccer ball in Winstons tutorial. that was over 10 years ago, wow time flies. I know your done with your project now, but if its any use to you or anybody else here's the drawing. I did have the full tutorial somewhere but cant find it.

Pjay

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* June 01, 2017, 09:30:23 AM
#25
Alvin,

I did not think anybody would be that interested in what I was trying to do. I did not mean for anybody to obsessed with a stupid soccer ball. I did not know what to think of the level to which it would take to do this.

Thanks,

Doug

Too late now, Doug. I'm hooked.

Henry H

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June 02, 2017, 07:40:54 PM
#26
I caught the bug too..... :-)

After seeing a renewed interest in the creation of a soccer ball on the TurboCAD forum I decided to look up Winston Mitchell's old V7 Soccer Ball Tutorial. With my own renewed interest I decided to create a video series using it as the basis. I hope that you enjoy it.

4 part Soccer Ball Tutorial Link

Playlist:
https://www.youtube.com/watch?v=ve6s6cGGNfo&list=PLAdJfVv2fDkRDAMgFtAiGdoahj0o37W0D
« Last Edit: June 02, 2017, 08:29:37 PM by Don Cheke »

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