Prism problem
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As long as we're looking things up on Wikipedia, we can see that it gives the dihedral (included angle between two adjacent faces) of a tetrahedron as 70.528779°. That gives us the following very simple construction:
~Voder
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@voder vocoder said:
As long as we're looking things up on Wikipedia, we can see that it gives the dihedral (included angle between two adjacent faces) of a tetrahedron as 70.528779°.
i think the challenge is to build the shape entirely using sketchup tools and locks.. the cube method makes this possible.. your solution uses math (albeit you went straight for the answer but 70.52....deg is a solution for an equation)..
here's an easy method for drawing an equilateral triangle without entering any numbers... [edit] - using this same method should work for for the entire shape but i'm having weird snap to problems.. i'll mess around with it tomorrow.. goodnight..
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I must have been doing something weird when i tried that cube method originally, works like a charm now.
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@remus said:
I must have been doing something weird when i tried that cube method originally, works like a charm now.
Okay Remus, a beer or two now for you or anyone else with %(#FF0000)[a correct method
with only SU, no math, to solve the problem attached to my previous post. No trial and error though,] I did that already. -
Wo3Dan, by what means did you place the guide point? What do you mean by "this could be endpoint A"?
~Voder
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@voder vocoder said:
Wo3Dan, by what means did you place the guide point? What do you mean by "this could be endpoint A"?
~Voder
Voder, interested in the beer, right?!!
I just placed a guidepoint (A’) on the vertical line, measured A’B and moved A’ up and/or down till I got the right length AB= 2102,833625??? mm From now on A’ is called A.
So this was done by trial and error, so to speak. And A is “only” accurate 6 decimals. Thereby it could be THE point A, the one I'm after.I want the red and yellow plane dimensions unchanged after rotation while they now have a common edge length AB=2102,833625xxx mm
But to be honest, I’m not really interested in being this precise. What I’m after is a decent
way to do a rotation/snap in any situation, something SU unfortunately seems to lack.
So a rotate/snap solely for the reason of better/easier 3D constructing.
Not everything is as regular as a tetrahedron.Wo3Dan
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@unknownuser said:
But to be honest, I’m not really interested in being this precise.
if you don't need super precision, you can use a heavily divided radius and it will get you pretty damn close if not right on the money..
2000 segments per circle here and the radii do in fact intersect..
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@wo3dan said:
Not everything is as regular as a tetrahedron.
True, including me, I'm afraid. But that's for a different forum.
@unknownuser said:
if you don't need super precision, you can use a heavily divided radius and it will get you pretty damn close if not right on the money.
2000 segments per circle here and the radii do in fact intersect.Jeff, I have taken your previous admonition to heart and agree that the purpose of these construction exercises is not just to get the job done by whatever means, but to work within the constraints of SU's tools and, by applying them in an ingenious and elegant manner, solve the construction problem. The tetrahedron-in-the-cube is such a solution, although no one here can take credit for it beyond finding it in Wikipedia. On the other hand, using a 2000-segment circle is not particularly elegant; rather, it's more of a brute force approach, wouldn't you agree?
Wo3Dan's problem is indeed vexing.
~Voder
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Update: Acknowleding that it's really the same kind of brute force approach as the 2000-segment circle (and with a nod and smile to Jeff), dividing the vertical edge containing point A into 1000 segments yields fairly accurate results with the Rotate tool (although you have to Zoom way in to see the best fit). Rotate doesn't seem to have any problem with inferencing an endpoint to another endpoint, only to On Edge.
~Voder
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@voder vocoder said:
On the other hand, using a 2000-segment circle is not particularly elegant; rather, it's more of a brute force approach, wouldn't you agree?
so what.. i said all that other crap before free beer came into the equation..
seriously though, you're right.. and, i really don't think there's any sort of efficient manner to do this type of stuff in sketchup.. it would need true arcs i think..
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or maths...
After spending half an hour on this, i tihnk if you want to try and do it withotu using the cube method youd be best of just learning pythagoras.
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Hi folks.
Some ideas on the "Cube" method in the attached SU file with an explanation on how to rotate the tetrahedron to have one side flat on the ground.
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Hi folks.
Just in case someone is interested in the Platonic solids (also called Pythagorean solids),
see these two SU file that show the relation between:1 - The cube or hexahedron (6 square faces) and the octahedron (8 triangular faces).
2 - The dodecahedron (12 pentagonal faces) and the icosahedron (20 triangular faces).
For each pair, you can get from one solide to the other by joining the center of each faces to the center of its neighbors faces.
For the tetrahedron, you will get another smaller tetrahedron if you use this procedure.
In conclusion:
1 - You can get the tetrahedron and the octahedron from a cube (see previous posts).
2 - You can get the icosahedron from three intersecting golden rectangles each at 90° from the others two as was shown in a thread somewhere.
3 - You can get the dodecahedron from an icosahedron.
Thus, you can get all five solids with great precision using only basic SU tools and without using any mathematics.
Just ideas.
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