First please excuse some missspelings i am a student from Germany.

My Project is based on your specifications and contains a cube with cylinders.

The main idea is to use o'neill cylinders to create gravity through rotation. Through this the plants know where up and down is. Also a big usable surface is createt by cylinders. More informations will be given in each step.

(I dont know why but the quality of the pictures reduced quite a bit on this platform exuses this please. But the main structure is still understandable)

Supplies

-box (growbox)

-wire

-air pipe

- cylinders

-led light

-watering system

-heating (optional)

-lots of electronic

-computer program (automatic watering lights etc.)

Step 1: Complete Box

This are the 3d models of a complete box with all cylinders just to get an idea of the look. After this overview i am going to explain every part alone. The brown part is the engine and the withe parts are the cylinders with the plants. The green parts are the plants which grow in a circle straight towards the light (pink).

Step 2: Box

The box is 50cm cube as requestet but can be bigger. You can make the box bigger or stack several boxes on each other to create on big box. Depending on the plant species you want to grow the cylinder needs to be bigger or smaler. The used material should be very light so some plastic or carbon would work. At the back are wires for power supply for all sytems like light or the Computer. Also the water for the irrigation system comes from there. In this box also an air supply pipe exists but if the box stands in a station with humans it just can be open. If it is in a living area the temperatur should be good but optional a heating on the bottom could be attached and controlled by the computer. Likewise a transparent door and a top should be used to create a consistens enviroment.

Step 3: O'neill Cylinders

The main idea is to use these cylinders to create a artifically gravity. Plants need gravity to root well because they got to know where up and down is. Only 0.1 g forces are needed so the plants know where they should root. This means the cylinders dont have to rotate fast which saves energy. The rotation presses the plants at the inner circle of the cylinder. This space can be filled with wadding or soil to create a ground for the plants. Over the wadding a grid can hold the ground in place but lets all the plants trough. As plants I choose cress because it can be grown very easy. For example only wadding is enough as a ground for cress. You can harvest and get fresh food every 7 days because of the fast grow. The cress is easy care and has a lot of vitamins. It can be grown on all sides of the cylinder because of no gravity so the use of space is efficient. All cylinders are connectet by gears so they rotate each others. One engine can power the hole box. In the center of every cylinder is a rod with the LED lighting. This should be a combination of red and blue (additionally green) to hit the most efficient wavelenght for plants growth. So now the best artfical sunlight is createt. It goes in every direction so all plants get light. But through the rotation it doesnt matter because oviously all plants are exposed to light at some point. Also at this rod the irrigation system is attached. It sprays water in the air which is automatically pressed to the outside of the cylinder by the artifically gravity to water the plants. All this light and water should be coputer controlled and fully automatic. But an astronaut should always keep an eye on the cress and controll everthing. Additionally fertilizer or pesticides could be sprayed out of this contraption but also can be added by hand. You can take out the cylinder completely and unfold it to acess the plants and harvest. During this process the rod stays because its atached to the box. The cylinder has a suspension on the back of the box and the used material should be very light so some plastic or carbon would work. Depending on how thick the wall of the cylinders is there should be 6 to 7 cm in hight for the cress wich is enough. If the cube is 50cm high 3 cylinders as shown in the model fit perfect. We lose a few cm to the cylinder walls and gear and to the light and water rod but the hight should be enough. Thereby the spaces is used very efficient because the cress grows until it alomst touches the rod and then can be harvest.

Step 4: Imrovement

In my model the gears are at the back of every cylinder which seems inefficient but in my 3d program i could not change that. To reduce the friction and power consuption of the engine ball gearings should help. Also an efficient suspension for the cylinders at the back is needed. Or to center the gear and bring it more to the front could improve the balance. All this is just the main idea. I let you guys at NASA figure out all the details. But some electronic stuff and computer programs shouldnt be a problem fo you.