How to draw a pyramid?

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1

Hello,

I want to draw a pyramid where
all sides are an equilateral triangle.

I’ve tried using planes at an angle,
and adjusting the angle after extrusion.
(if I only knew the exact angle? )

So, 4 sided, all sides a triangle with
equal length sides.

Any ideas?

ps. new here, if this is the wrong forum,
movie it please.

2

Take at at this posting above.

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3

How I did it:

The trick is to make a circle with the same radius as the length of the sides in one of the bottom corners of a square cupe cut in half diagonal. Then rotate the circle 45 degree so it ends up on the diagonal face.
Then draw a center line on that face and trim it of on the circle.
There you will have the correct height of the Pyramid.
Project this to the sides and use it to make a triangle on two sides so you can subtract this from a cube.

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4

If you need detailed pyramid, here some solution:
With loft, as my tetrahedron , you can set the angle of the sides…

Or sculp, like my octhedron …

Regards:
A

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5

Find height of the desired pyramid (see below). Draw a square. Extrude the square to the height “h” of the pyramid. Select the top surface of the extrusion and scale it to 0%.
Pyramid

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6

My first method was to find the height too. Not using that formula but just using regular Pythagoras.

Basically you first find the height of a triangle with pythagoras and then that height will be the Hypothenus of a triangle to the center, That again will give you the height of the pyramid.

But because of desimals rounding up the sides was 449.99991 instead of 450 as it should b e

A better way was to use geometry instead and have shapr3d do the calculations.
Just cut a cube in half and make a circle on the diagonal face with the same radius as the length of the sides. Then draw a senter line and the intersection will be the true height of the pyramid. You can then cut the line at the point and project it to two of the sides to make two triangles you can extrude/subtract.

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7

Good tips guys, very useful to know.

8

Thanks for the great ideas.
It’ll take a little while for me to try each one,
I’ll get back to you then.

9

I!ve made the loft version for pyramid.
If you need another parapameters ,you can “stand” up any kind of triangle.

R,
A

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10

Here’s another way.
(Sorry about the speed. I had to speed it up to fit in 10mb.)

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11

If only they could have built the Great Pyramid that way :grin:

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12

And here’s a variation using Intersect.

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13

This has turned into a great thread guys. :+1:

15

Not sure if anyone already demonstrated this method, but this seems like the easiest way to me. It is hard to be exact since there is some rounding but it will be pretty close.

  • Draw Cube
  • Split Diag
  • Draw line (h) from midpoint to corner (this is the same length as a base to the height of pyramid)
  • Extrude cube same height as length of line (h)
  • Scale top of cube to zero, you may have to “delete” final flat bit if you can’t get it to scale down to zero
  • Measure sides. Result is based on how precisely you can measure line (h).

16

I have to confess I asked my question wrong, to begin with.

I was trying to draw a pyramid with a triangular base,
and 3 sides triangles, all equilateral. I said all for sides
as triangles. But I meant all 3 sides and the base.

I accidentally said all 4 sides.

I didn’t realize this is a “wolfram” thing.

google-ing I found this:
A triangular pyramid is a [pyramid] having a triangular base. The [tetrahedron] is a triangular pyramid having congruent equilateral triangles for each of its faces.

What I really wanted to know is if you could make
this thing and all the angles would be 60 degrees.
I couldn’t see why not. But I could not figure out how
to shapr3d draw it.

These videos and this discussion is very interesting.

My useful knowledge is pretty much zero.
But I guess I was asking how to draw a tetrahedron
with congruent equilateral triangles.

I had no idea this was what I was asking.
And I still have no idea how to shapr3d draw this.

17

See my post above,my first vid with loft, or
An another solution:

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18

Here’s a way. The cube is rotated 30° so the sides of the pyramid will be 60°.

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19

I finally found some courage to try
some of the many, great examples.

I started with TigerMike Aug 9, fast video,
failed! -my skills lacking
I found myself upside down regarding the 3D axis,
after the initial setup,
then apparently extruded the wrong way.

After some sulking, I tried JST’s Aug 8,
loft-tetrahedon - success!!!
A little stumbling on the lofting,
I didn’t see to loft 3 times, at first,
I was trying to loft all at once.
And I tried to copy at the end,
instead of moving the union away from the sketch.

But this is my favorite method, so far.
It’s elegant, because it’s simple.
And I’m simple, and that’s why I like it.

I tried, on my own, to extrude, 3 times,
around the horn, then solid subtract,
and failed miserably. I see JST has
presented this method, I think, and
will try this next.

I also failed, trying to extrude the
equilateral triangle, up a leg length(10mm),
then sweeping, 19.4555 degrees.
I kept getting only as close as 10.0058
for sides length. 19.46 would overshoot
I don’t understand this sweep thing.

And since I thought my side length,
wasn’t closing the top cap, I pinch
zoomed in to the cap, and noticed
what looks like an opening.

But then on the loft method pyramid,
with exact 20mm on all sides, this
supposed opening is there also,
when extreme pinch zooming.
So, I don’t understand this either.

Apologies for the delay.
My embarassing lack of skills,
I think, kept me from trying again.
Knowing a thing doesn’t seem to take any courage,
but it seems that pursuing that knowledge does.
Or, I’m just a coward. I always did think I was.

-many thanks!

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