How to model an equilateral triangular pyramid?

Question

How to create triangular pyramid with equal length of edges?

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.

Answer 1

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:

Delete Them to get this:

Step 3: Select one vertex on the edge.

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

To get this:

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

This icon should look like that:

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

You should end up with this:

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:

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.

Answer 2

Add a cone: 3D View header > Add > Cone

Change Vertices to 3

For Depth enter sqrt(2) and hit return

Answer 3

The vertices of a cube include the vertices of a tetrahedron, the math name of an equilateral pyramid.

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.

Answer 4

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.

Answer 5

• 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