The geometry of the the Sphere² Lamp is based on a Goldberg-Polyeder with 122 faces, specifically the Class II (2,2) polyhedra.
The ratio between the diameter of the sphere and the balls placed on its surface is 25:4. This allows to use standard 40 mm table tennis balls cut into half and placed on the surface of a 25 cm diameter styrofoam sphere.
- Hollow styrofoam ball, 25 cm in diameter, consisting of two separable halfs
- 61 table tennis balls, 40 mm in diameter, plain white
- 122 adressable RGB LEDs, e.g. from a WS2812B strip
- Microcontroller, e.g. Arduino Nano
- Power supply, 5V, ~15W, with connector
- Wire
- Optional: 470 µF capacitor for circuit protection, 220 Ω resistor
- For control via bluetooth: Arduino Nano 33 BLE, 1 kΩ and 2.2 kΩ resistors
- Soldering equipment
- Glue suited for styrofoam (solvent free)
- Compass for drawing circles
- Box cutter, scalpel, fretsaw or similar
- Pen & paper
The image below shows the spherical grid used to mark the positions of the LEDs (white dots) on the sphere.
The black equilateral triangle with side length a is repeated 5 times each on the norhern and southern hemisphere, and 10 times around the equator with alternating orientation.
Its height is b and the radius of its inner circle is h.
The length of the segments can be calculated using the half side formula,
which yields for a sphere of radius R = 12.5 cm:
a = 1.107 R = 13.84 cm
b = 1.017 R = 12.72 cm
h = 0.365 R = 4.56 cm
The LEDs are places on the sphere as shown by the white dots in the image. The distances between two neighbouring LEDs is either of (b-h)/2 = 4.08 cm, e = 4.28 cm or h = 4.56 cm (where e can be calculated using the spherical law of cosines). Therefore balls of 4 cm diameter are choosen to cover each LED.
To mark the positions of the LEDs on the sphere, it is useful to prepare two marking aids. On a small strip of paper (or two), mark these distances:
a/2 = 0.554 R = 6.92 cm
(b-h)/2 = 0.326 R = 4.08 cm
h = 0.365 R = 4.56 cm
For either half of the styrofoam ball:
- Identify the north (or south) pole and mark it
- Divide the equator (the edge of the half styrofoam ball) in 5 equal segments of 2πR/5 = 15.71 cm arc length each
- Place the first marking aid from the pole towards the equator for each of the 5 directions and mark the indicated LED positions in blue or green
- Mark the center between each two neighbouring blue marks (at a/2) by using the first marking aid
To identify the positions on the equator, put the two half spheres together and connect two blue marks on either half. 10 LED positions will end up exactly on the equator, it is best to mark five of them on either half of the styrofoam ball.
Now that all positions on the black triangles are marked, proceed with the second marking aid.
- Place the ends of the second marking aid on two of the blue marks
- Mark the remaining distances as indicated (along the red line)
- Repeat this process until all positions are marked.
To identify the positions near the equator, put the two half spheres together and connect two blue marks on either half.
After all 122 LED positions have been marked, use a compass with two peaks set 2 cm appart and carve a circle around each marking. This will help correctly positioning the balls later.
Number the LED positions as shown below, corresponding to the indices used in the code. It is important to connect the LEDs in the correct order for the animations to work, since each LED number is associated with its position on the sphere.
An interactive 3D model that helps with the assignment is provided in the Jupyter Notebook spherical_geometry.ipynb or alternatively online.
Glue the LEDs on the marked positions. For the LEDs on the equator, stick 5 to the northern half of the styrofoam ball (numbers 57 to 61) and the other 5 to the southern half (numbers 62 to 66). You might want to position the pole LEDs (number 1 and/or 122) slightly off center or omit them in favour of a mounting for the lamp.
Connect the LEDs from number 1 to 61 and 62 to 122 using your soldering equipment. Stitch the wire through the styrofoam such that the cables won't be visible in the gaps between the table tennis balls later on. Route the power wires from inside the hollow styrofoam ball stitching them through the sphere. Use the connector that came with the LED strip to create a detachable connection (data + power) between LED 61 and 62 inside the sphere, allowing you to take the half spheres easily appart.
Connect the power supply (5V and GND wire) near the center of the LED supply chain, e.g. near LED 61. The data input of LED 1 will be connected to pin D11 of the Arduino, with an optional 220 Ω resistor. A 470 µF capacitor near the power supply is used to protect the circuit against voltage spikes.
At this point, it is a good idea to test the setup.
This includes checking the connections with a multimeter and then powering up the circuit and confirming the functionality of each LED and their correct order (or adjusting the order in the code).
Check the heat generation and power consumption by running all LEDs on maximum brightness and white color for half an hour or so.
You can use the functions anim_count(); and fill_solid(leds, NUM_LEDS, CRGB::White); from the provided code for testing purposes.
The table tennis balls need to be cut (or sawn) in half. Typically these balls have a seam from their fabrication which becomes clearly visible when shining light through them. When cutting the balls, make sure to cut close to this seam, so that it is not visible when the balls are illuminated by the LEDs.
To help cutting the balls in half, a marking aid can be build by rolling a paper strip of 6 cm width around one of the balls. Every other ball inserted into the resulting tube on top of the reference ball can easily be marked at its middle.
Glue the halfened table tennis balls to the styrofoam ball using a suitable, solvent free glue (otherwise the solvent will dissolve the styrofoam!).
To control the lamp over bluetooth low energy (BLE) using a smartphone, the Arduino Nano 33 BLE is used. Unfortunately the FastLED library used to drive the adressable LEDs is not compatible with this board. Therefore, two boards are used: The Arduino Nano 33 BLE is connected to the Arduino Nano via a serial interface as shown in the circuit sketch below. While the Nano drives the LEDs, the Nano 33 BLE handles the BLE connection, communicating with the Nano over serial. The voltage divider takes care of the logic level conversion (5V for the Nano, 3.3V for the Nano 33 BLE).
The serial interface also allows to control the lamp with any other device, e.g. from a computer over USB.
Here is an image of how the resulting Sphere² Lamp looks like.
