Connect face to edge

Hi, all. I’m trying to construct simple geometric shapes, but I’m running into an issue when it comes to constructing shapes with irrational dihedral angles.

In the attached image, I am attempting to construct an equilateral trigonal pyramid whose base edges are of length 1 and whose isosceles edges are of length (1 + √5)/2 (φ). The irrational side lengths are easy enough, but I can’t figure out how to connect them.

In the image, the edge lengths are constrained, but I want the top edge to connect to the top vertex of the base, essentially rotating the edge and the face until the red line shrinks to 0.

Any help would be greatly appreciated.

Hi Dent,
If you add a construction plane using 3 points, you can then sketch on that plane. I think you have all the points you need.

My approach to creating your “golden rectangle pyramid!?!” is to create one right triangle and rotate it along the long leg. By copying and rotating twice at 120 degrees, you build a “frame”. Then you can add construction planes using the 3 point method to define the faces of the pyramid.

I did something like that, then made a triangular prism body and used the planes to split that body.

You are 30 seconds ahead of me. Yes, 3 points to make a plane works.
(We’re on the same page)

May be this method is help

Or this:

Edited the length ( (1 + √5)/2) then continue as vid before, with loft can get the full body.

Incredibly helpful! And synchronized! Lol

@TigerMike My goal was not to create that edge (I had already done so), but for that edge to be set to a length of 0, essentially “pulling” the existing edge and the equilateral triangular face together.

I’m not sure why this isn’t achievable using only constraints, but the proposed methods are simple enough.

Thanks again, y’all!

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You are welcome, glad we could help!

And I present:

:drum: :drum: :drum:

The golden triangular rhombohedron!

(still image bc I’m not allowed to upload videos yet)

Speaking of which, a simple auto-rotate feature in visualization mode would be really nice for quickly showing off a piece with a looping GIF

Cool! A video would awesome!