adobe photoshop - Designing repeating pattern for top section pyramid

I have a requirement that I am failing to figure out.

I am trying to design for a print item shaped as a pyramid, where each top (triangular) sections of the pyramid will have some repeating floral or other pattern (Illustrator or Photoshop)...

I would have no issue if it the top part formed a square, but it isn't quite a square.

The design surface I will be working with is one side of the pyramid, which will then be printed 4 times then assembled.

I have attached an image to better illustrate what I would like to do:

Answer

See the picture:

Your pyramid has 4 equal triangles. The top part is separated by a horizontal line. The top part can be considered as a part of the surface image, so I have not drawn it here.

Note: The bottom face is ignored in this answer.

Anything that is reflected equally to the left and to the right from the white center line of the triangle will continue seamlessly around the pyramid.

Altenatively you can position your 4 triangles side by side onto your artboard and draw over the seam. The leftmost and the rightmost edges must be fitted separately. The fitting is automatic if you have a symmetry line between the triangles 2 and 3. See an axample:

The green line is the symmetry axis. The red piece of art will continue seamlessly around the pyramid.

How to get the wanted height H and the wanted bottom side A:

• calculate a temporary length S = squareroot(H^2 + (A/2)^2). Actually this is the length of the white centerline.


• the angle X = 2*arctan(A/(2*S))


• B = S/cos(0.5 * X)

The calculations are not a must, if you do not need exact height. Then draw one triangle (=the orange in my picture), sketch the white centerline and draw a symmetric pattern onto the triangle. Then make three copies and you're done.

Note: A tetrahedron needs only 2 copies.