Optical Illusions can use color, light and patterns to create images that can be deceptive or misleading to our brains. The information gathered by the eye is processed by the brain, creating a perception that in reality, does not match the true image. Perception refers to the interpretation of what we take in through our eyes.

Optical illusions occur because our brain is trying to interpret what we see and make sense of the world around us. Optical illusions simply trick our brains into seeing things which may or may not be real.

In this instructable I will create a sculpture made up of 3 plastic mosaics that easily fit together on a plane, giving the view the 3-dimensional sensation of being stacked cubes.

In this instructable I chose red as the color of one of the diamond-shaped mosaics, combined with black and white. Since these last two are considered neutral colors, the human eye also perceives the color red as the main one.

But alternatively, other colors can be used instead of red such as yellow, blue, green, purple, etc. combined with neutral colors such as white and black and gray or softer color variant of yellow, blue, green, purple, etc.

In addition, with this system of plastic mosaics that are joined together, you can create an alternative sculpture in another way (see Design step 3).

Let's do it!

Step 1: Supplies and Tools

Supplies:

Filament PLA red color.
Filament PLA white color.
Filament PLA black color.
Wooden thickness 25 mm.

Tools:

Printer 3d.
White Matte Spray Paint.
Sanding Sponge or Sandpaper.
Wood Router Machine.
Straight end mill milling cutter flutes (tungsten Steel) 1/2 ”cutting diameter.
Table saw or Jigsaw table.
3D Printer Cutting Pliers.

Step 2: About the "reversible Cubes" Illusion

In geometry, the rhombille tiling, also known as tumbling blocks, reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Each rhombus has two 60° and two 120° angles; rhombi with this shape are sometimes also called diamonds. Sets of three rhombi meet at their 120° angles, and sets of six rhombi meet at their 60° angles.

The rhombille tiling can be interpreted as an isometric projection view of a set of cubes in two different ways, forming a reversible figure related to the Necker Cube. In this context it is known as the "reversible cubes" illusion.

A tessellation or tiling of a flat surface is the covering of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions and a variety of geometries.

A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner identically arranged.

A real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons. Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor or wall coverings. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the Moroccan architecture and decorative geometric tiling of the Alhambra palace.

Tessellations are sometimes employed for decorative effect in quilting. Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.

You will also see that there are hundreds of variations of this optical illusion (photo 3).

Credits:

Photos by:

- Institute for the Study of the Ancient World - Houses on Delos (XLII) Uploaded by David Eppstein.

- Tomruen - Own work, CC BY-SA 4.0.

Source:

https://en.wikipedia.org/wiki/Mosaics_of_Delos

https://www.illusionsindex.org/ir/necker-cube

https://www.wikiwand.com/en/Rhombille_tiling

Step 3: Design

I used Autodesk fusion360 and Adobe Illustrator for design.

On a plane I drew a hexagon 15 mm per side that I divided into three equal diamonds. Then, when they were extruded 7 mm, they became thick: white on the top, black on the left and red on the right.

I decided that the three diamonds join each other and with others through the joint system used in wood carpentry called "mortise and tenon joint".

For the joints I took as a premise that the mosaics were growing as they fit from left to right and from bottom to top.

In this way, two types of diamonds "A" and "B" were formed by the configuration of their joints.

With the final design of the type "A" diamond, the black and white diamonds can be printed on a 3D printer, while with the type "B" the red diamond can be printed.

The type “A” diamond has two “tenon” type (male) connections on two side walls of the diamond that form a 120 degree angle between them and two “mortise” type (female) connections on the other two remaining side walls of the diamond. .

The "B" type diamond has two "tenon" (male) type joints on two side walls of the diamond that form a 60 degree angle to each other and two "mortise" type (female) joints on the other two remaining side walls.

The dimensions of each “tenon” (male) joint is 9mm x 2mm x 3mm.

The dimensions of each “mortise” (female) joint is 9.2mm x 2.30mm x 3.05mm.

To build a hexagon, start with the three diamonds placed as indicated in the figure (black on the left, white in the center, and red on the right).

The white rhombus is taken and turned 90 degrees counterclockwise and placed on top, while the red rhombus is taken and brought closer to the black one.

In this way, from left to right and from bottom to top, you can follow exactly the arrangement and quantity of hexagons that I chose in my case, or choose your own. Believe me, it is very fun and easy to build the figures according to your own imagination.

You can also alter the colors of the diamonds or even add other additional colors. For this I suggest that prior to printing in 3d use to test the file in Adobe Illustrator that I attach with this instructable.

To support the plastic sculpture formed by all the hexagons embedded together and support it on a horizontal surface, I decided to do it with a 150mm x 48mm x 25mm hardwood with a 7.5mm x 5mm "U" shaped milling. The finish I gave to the wood was painted in a matte white color.

The stl files are included in the next step.

I have included the file Cubes Illusion Scupture TEMPLATE.ai in Adobe Illustrator with the sculpture design included in this instructable. You could change the position of the hexagons by adding or subtracting, altering the way they are joined together, and also changing the colors. Color styles have been created (See Adobe Illustrator screen print screen). See Images: Blue Light Model / Orange Model / Yello Model.

Credits: photo "How To: Make a Mortise and Tenon Joint" by Bob Vila

Step 4: Summary of All Task

To make this project, once you have the necessary materials and tools, the tasks are as follows (then they will be explained in more detail in step 5,6,7 y 8):

3d printing (step 5)

3d print 25 diamonds with red PLA filament.
3d print 25 diamonds with white PLA filament.
3d print 25 diamonds with black PLA filament.

Build the Support Base (step 6)

Build and paint the wooden support base

Build the Sculpture (step 7)

Assemble 25 hexagons joining the three diamonds of each red, white and black color.
Fix the 25 hexagons together to form the sculpture.
Fix the sculpture on the base.

Placing the sculpture (step 8)

Find a good place to display the artwork.
Enjoy.

Step 5: 3d Printing

The sculpture I made is made up of 25 hexagons, so you must print in 3d 75 diamonds:

25 red (primary color).
25 white.
25 black.

With the attached STL files you can export to the program you use to define the printing parameters (CURA, etc.) and export to GCODE:

With "Diamond A.stl" to print black and white diamonds

With "Diamond B.stl" to print red diamonds.

The print was made with PLA filament on a 3d printer.

The main parameters that I used were:

Layer Height = 0.12 mm.
Infill = 15%
Bed temperature = 65/70 degrees.
Nozzle temperature = 195/200 degrees.
Printing speed = 35/40 mm / min.
Generate support = no

TIP1: for “tenon” parts, I used support "cones" (see the photo) to ensure that the support adheres better to the base. Download "Custom Support" plugin by Krasimir Stefanov. You can download in the Cura MarketPlace.

TIP2: in Cura, menu top/bottom, set "enable ironing" to that the surface of the top layer of the printed diamonds has a smooth finish.

TIP3: The final dimensions of the “mortise and tenon joint” were defined after doing many tests printing and embedding the diamonds and seeing that the union was easy but safe. I suggest that before printing all the pieces make an impression of a diamond of each color and test the fit. If necessary, you can adjust the dimensions of the "tenon" / "mortise" parts as necessary to improve the joint. Below is a link in Autodesk where you can access the 3d file.

I also recommend before printing to perfectly level the bed, so that you can print batches of a maximum of 10 diamonds of each color at a time.

Once the parts are printed, remove the supports, and use the 3D Printer Cutting Pliers to remove imperfections in the print, etc.

Step 6: Build the Support Base

To build the support base:

- I used 25 mm thick hardwood.

- I cut a piece of wood L=150 mm x W=48 mm x H=25 mm (see photo 1, and plan photo 2).

- Proceed to sand (see photo 3)

- Mill the notch in a “U” shape using a hand router in the shape of a router (see photo 4)

- The bit I used: straight end mill milling cutter flutes (tungsten Steel) 1/2 ”cutting diameter (see photo 5)

- Note I used the accessories that came with the Wood Router Machine: metal guides to support the wood and set the exact distance to do the milling (see photo 6 and 7).

- Sand to a smooth, flawless surface.

- Paint with white matte spray paint.

Step 7: Build the Sculpture

With all the pieces printed in step number 5, to continue we will proceed to build the sculpture by fitting the colored parts together following the design of the photo.

To build a hexagon, start with the three diamonds placed as indicated in the figure (black on the left, white in the center, and red on the right).

The white rhombus is taken and turned 90 degrees counterclockwise and placed on top, while the red rhombus is taken and brought closer to the black one.

Repeat the same procedure to form 25 hexagons.

Join the hexagons from left to right and from bottom to top, following the arrangement and quantity of hexagons that I chose in my case, or you can also choose your own, join more quantity of hexagons, etc.

Believe me, it is very fun and easy to build the figures according to your own imagination.

Once they are finished fitting the hexagons, fix it vertically in the “U” notch of the wooden support.

Step 8: Placing the Sculpture

Now to enjoy decorating either at home or in the office.

It can be part of the modern decoration on low tables in a living room, or they also look great on home or office desks.

If you have it near you on your desk you may be tempted to modify its shape and perhaps use it therapeutically :)

Alternatively, you could glue rubber magnets to the back of the sculpture to fix it to a metal surface such as a refrigerator.

Alternatively I have printed with another color combination (yellow primary color, and gray and black neutrals) so you can see what it looks like too.