# 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:

• I'm not sure I understand; what exactly is the problem you're having?
– Cai
Commented Feb 19, 2017 at 18:31
• Hi Cai. Thanks for the response..Sorry, it's hard for me to explain. I would like to have a repeating, seamless pattern in the Green triangular area, such that if I print and cut 4 copies of the entire triangle, then assemble them in a pyramid, the repeating seamless pattern will not be broken Commented Feb 19, 2017 at 18:35
• Oh I see, you need the pattern to repeat around the whole pyramid but your pyramid is made by duplicating the same triangle, yes? Conceptually it shouldn't be any different than making any repeating pattern. I'll see if I can work an answer for you when I've got some more time later.
– Cai
Commented Feb 19, 2017 at 18:40
• Do you already have a pattern or are you creating the pattern yourself?
– Cai
Commented Feb 19, 2017 at 18:41
• That's it exactly!!! The shape from the top is not really a flat square, so I thought the seamless design is done slightly differently Commented Feb 19, 2017 at 18:41

## 2 Answers

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.

• Wow, very detailed explanation! Commented Mar 16, 2017 at 20:49
• @user919426 actually the angle X has been 50% too small for 3 weeks without anybody noticed.. It's now ok (= inserted 2*)
– user82991
Commented Mar 16, 2017 at 21:55

If it is a 4 sided pyramid then the green area will appear square when viewed from above.

You can make the 4 triangle faces by bisecting this square with the pyramid edge lines:

Each face of the pyramid is a right triangle with the right side at the top.

Draw your pyramid from above (square) with the top (green) section a smaller square centered in the larger one.

Bisect both with 45 degree lines (I drew a vertical line, copied it, pasted it, rotated new one 90 degrees, selected both, aligned horizontal and vertical, rotated 45 degrees and placed on my squares, then aligned Everything horizontal and vertical using Align to Artboard - with a square Artboard).

Apply a continuous pattern in the center square. When you are satisfied you can use the angled lines to divide the whole image with (Select All) Pathfinder-Divide or make a triangle that perfectly covers one of the faces and isolate just the one side for printing by using that triangle to make a clipping mask (Group All except new triangle, select group and new triangle, Left Click - Make Clipping Mask)

If it is a 3 sided pyramid the process is the same but with different shapes. Let me know if should illustrate that one.

• A face having 90 degrees top angle is not possible if the pyramid is symmetric, has a non-zero height and has 4 planar triangular faces. You might want to do some edit. 3 of your triangles can belong to a tetrahedron.
– user82991
Commented Feb 20, 2017 at 18:12
• Yes I realized after I answered that some vertical stretching of the face will be necessary. The fact that a four sided pyramid is square from above so can be worked as a square is a valuable insight into this persons problem. Unfortunately there will be some distortion when vertically adjusting the faces. This distortion can be managed multiple ways. If I was printing a pyramid this is the way I would do it, I'd just figure out how to resolve the distortion. Thanks for your input. LOL @ non-zero height. Commented Feb 20, 2017 at 18:44