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How to create triangular pyramid with equal length of edges?

enter image description here

Note - I'm not looking for a way to create one with a single click, but I want to be able to model one from scratch.

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  • $\begingroup$ David - That is about 4 sided pyramid. This is about 3 sided. $\endgroup$ – Vladimir Jun 14 '14 at 1:04
  • $\begingroup$ cegaton - That question is about creating, not modeling from scratch. This other answers are explaining the modeling (I think), but I don't understand quite well. Might be my lack of english. $\endgroup$ – Vladimir Jun 14 '14 at 1:05
  • $\begingroup$ See here $\endgroup$ – Robin Betts Aug 1 at 19:03
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Note: There are superior ways to perform this task, but the question asked to be shown how to model an equilateral triangular pyramid from scratch.

Step 1: Add a plane.

Step 2: Delete all edges except for one.

Select these two verts:

enter image description here

Delete Them to get this:

enter image description here

Step 3: Select one vertex on the edge.

Step 4: Hit Shift-S, and select: Cursor to Selected

To get this:

enter image description here

Step 5: Hit Period. (Not on the number pad)

This icon should look like that:

enter image description here

Step 6: Select The edge, and hit Shift-D then R then Z then 60.

You should end up with this: enter image description here

Step 7: Select the other vertex on your original edge repeat step 4, and then repeat Step 6. If the edge when the wrong way, undo your last move, and use -60 degrees instead.

Once complete your scene should look like this:

enter image description here

Step 8: Hit W, and select remove doubles.

Now you can see that we have the base of the primid

Step 9:

Select the base and hit Shift-D then R then X then 70.5288.

One side is now in place

Step 10: Select the side that we have created, duplicate it (Shift-D), and rotate it 300 degrees along the z - axis.

Step 12: Remove all doubles.

Note:

If the top vertices don't merge, select them and hit alt-M, and chose center.

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  • $\begingroup$ Can you reexplain step 5? What do you mean by "Period"? I know this might be a stupid I ask, but I need to study some English terminology. $\endgroup$ – Vladimir Jun 14 '14 at 1:20
  • $\begingroup$ its the key with a dot on it: . $\endgroup$ – GiantCowFilms Jun 14 '14 at 1:22
  • $\begingroup$ Ok, thanks. My English is not very bad, but I asked because in terms of Blender it might meant something else. $\endgroup$ – Vladimir Jun 14 '14 at 1:59
  • $\begingroup$ @Vladimir Okay, very happy to help. $\endgroup$ – GiantCowFilms Jun 14 '14 at 2:00
  • $\begingroup$ And if possible some screenshots, 'cause It confuses me a little. $\endgroup$ – Vladimir Jun 14 '14 at 2:00
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Add a cone: 3D View header > Add > Cone

Change Vertices to 3

For Depth enter sqrt(2) and hit return

Add Cone Tool Shelf

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  • $\begingroup$ Thanks. I didn't know you can answer after the accepted answer, but cool. (Don't get me wrong. I really didn't know that). $\endgroup$ – Vladimir Jun 14 '14 at 9:51
  • $\begingroup$ Answers can always be added and up/down voted, unless the question is put on hold or closed. You can even change what the accepted answer is as questioner. $\endgroup$ – CoDEmanX Jun 14 '14 at 16:48
  • $\begingroup$ Where do you change Vertices to 3? I cant seem to find that. $\endgroup$ – chrismacp Jan 28 '17 at 18:06
  • $\begingroup$ It's at the bottom of the tool shelf, Add Cone. If it's not visible on the left-hand side of the 3D viewport, press T. I added a screenshot to my answer. $\endgroup$ – CoDEmanX Jan 28 '17 at 21:15
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The vertices of a cube include the vertices of a tetrahedron, the math name of an equilateral pyramid.

Connect the selected verts, delete the others

From a front orthogonal view (numpad 1), in edit mode, wireframe, select the upper right vertex.

Shift select the left bottom vertex, and then f to put an edge between the vertices.

Press numpad 3 to change the view, and add the diagonal from the upper left to bottom right vertices.

Press numpad 7 and create the diagonal from lower right to upper left.

Select and delete all four unused cube vertices.

Select all (A key) vertices and press f twice.

The tetrahedron is complete but not positioned.

Switch to object mode, solid view.

From front view, rotate the tetrahedron on y axis +-45 degrees until nearest edge is horizontal. In side view rotate on the x axis until this same edge is horizontal (35.18?? degrees).

The tetrahedron bottom is in an x-y plane.

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  • $\begingroup$ This answer would benefit a lot from a couple of screenshots. You also seem to have duplicated part of your instructions. $\endgroup$ – Sazerac Aug 1 at 23:43
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I'm fond of euclidean geometry. So instead of starting with a 3 point "circle"; The interior angles of a triangle Always add up to 180 degrees.

Topview

Change pivot point to active element. Create a line along X or Y axis. Set selection mode to points. Select the line with one point active (white). Shift D copy and rotate 60 degrees. Select original line. Make active point the opposite one from the first time you selected it. Same routine. You have an equilateral triangle. Select all points and remove doubles. The edge that is aligned along an axis is the one that must have the active element point in it.

Topview

Select the point that doesn't have lines along an axis. Extrude it through the triangle. Change to object mode. Rotate object so that a different side aligns to an axis. Edit mode. Select the point that doesn't have lines along an axis. Extrude it through the triangle until it's real close to earlier extrusion (bisect line). Zoom in and move the newest point, along extrusion axis, until it directly intersects the earlier extruded line. Front view. Extrude along z axis, up higher than size of triangle. The length of it means nothing if it's longer than the triangle.

Top view. Select triangle, active point on the line oriented to an axis. Change view to front or side so that the line points directly away. Duplicate and rotate until upper point comes close to upward pointing line. Zoom in and line it up perfectly.

Delete the extruded vertices. There's 3 of them. You have two triangles in the correct relationship. You can use line select and make faces. Select all after correct faces exist. Remove doubles. Done.

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  • Start with an edge of 1 meter
  • Extrude it along Z of 1/sqrt(2) meters
  • Triangulate the face
  • Duplicate all and rotate around Z of 180 degrees
  • Select the top vertices and rotate them 90 degrees around Z
  • Merge by distance

enter image description here

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  • 1
    $\begingroup$ @AlexD, thanks, but I'm not talented and Blender and things around it are just a hobby for me. You should ask on forums instead of BSE for this kind of things, IMO. $\endgroup$ – lemon Aug 3 at 17:30

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