I know there are lots of infinity gizmos out there - so here is another!. I found it easy to make and it usually gets a good "Wow!" I assume that anyone making theses has basic skills (mine are pretty basic!)

In the basic form of the infinity mirror you place an LED between a mirror and a half mirror to produce the infinity effect, in this version you have a mirror box - an LED and a larger half mirror box on the outside. the LED is in a strip that can be any shape and produce many effects, the two I show here are the corner strip and the tube strip.the boxes are made on a laser cutter using the Box-designer or other such app.

Step 1: Materials Needed

1. 3mm acrylic sheets - I use an Epilog laser cutter with a 12" x 24" bed so I use that size of sheet. You need clear sheet for the half mirrors, mirror sheet for the inner mirror and coloured sheets for the base.

2. LED light strips - 10mm wide indoor strips are the cheapest and come in several colours, if you want to be fancy the multicolour changing strips with remote zapper give great results but if you are soldering the connections it is twice as many joints. the strips usually come with

3. Shape former for the LED strips - I 3D printed mine (sorry!) but they can be made from strips of acrylic or, in the case of the circular shape a circle cut from a PVC pipe of suitable diameter.

4. Half mirror plastic film - this is widely available as the half silver film used to darken auto windows etc.

5. Power supply - 12v 2A supply for the LED strips, these are standard and also widely available and usually have a 2.1mm x 5.5mm male jack connector

6. Connectors - to connect the power supply jack to the LED strips I just used a 2.1mm x 5.5mm female jack and soldered but you can get ready made connectors which can connect a female jack to multiple LED strips.

7. Glue - I used the thin liquid acrylic solvent glue that uses capillary pressure to penetrate the joint. It is easy to find on eBay etc.

Step 2: Make the Inner Mirror Box

Decide on the size of the cube you want, basically you need an inner mirror cube then a space for the LED strip about 12mm deep and then an outer cube of half mirror.

For the inner mirror box I used a 180mm cube, to do this I used Box Designer

Box designer.connectionlab.org. You just input the cube size plus the material thickness and the software produces the PDF file for editing.
We only need 5 sides of the cube as the base needs to be empty. The Box designer app produces a notched edge which we need to straighten, to do this you need to use the drawing software you use for your laser cutter, I use Corel Draw and it takes about 5 minutes.

Step 3: Make the Half Mirror

There are numerous Youtube videos on how to apply the half silvered film, I found them useful but needed a bit of practice, the secret, for me, was to use lots of soapy water and a good wide squeegee and be meticulous about cleanliness.

Take the protective film from the clear acrylic sheet at the last moment and watch out for the static attracting any dust.

Once you have produced some acrylic sheets coated with the half mirror film allow to dry for about 24 hours. To make the cube you first need to calculate the correct size. If the inner mirror cube is 180mm a side then we need a gap of about 12mm for the width of the LED strip plus the width of the acrylic 3mm I.e. 15mm. We need therefore 180mm + 2 x 15mm for the width of the "cube" = 210mm. We also need 180mm + 15mm for the height = 195mm. So we need to tell Box Designer to draw a box 210mm width and depth and 195mm height.
When we have this drawing we need to straighten the base of the sides as we did for the mirror cube. Cut and glue the cube.

Step 4: Make LED Strip Formers

the formers are 10mm wide strips of plastic that the LEDs are stuck on to, I 3D printed mine but they can be simply made by cutting straight 10mm strips from acrylic sheet for the square ones or by cutting a 10mm section from a suitable pipe for the round ones.

For the corner strip lamp you need 5 x squares to fit onto the 5 surfaces of the mirror cube so for a 180mm cube 4 x 170mm x 10mm strips can be glued together to make each square.

For the tube lamp I used a 100mm diameter 10mm deep circle, I printed a spacer on each circle as shown in the photo but it turned out that they were not needed.

The LED strips I used could be cut at 100mm lengths so I tried to make the formers fit multiples of 100mm.

Step 5: Attach LED Strips to the Formers

For the square formers measure out a length of the LED strip to fill the inner surface of the former square, and solder about 300mm of connection wire to the terminals at one end, these wires are going to be lead into the inside of the mirror cube. You can buy LED strip connectors that just clip onto the end of the strip, these make the job very simple and they are not expensive, I used solder because I needed the practice.

For the round formers I used different coloured LED strips for the inside and the outside, this requires you to solder two contact wires to the inside strip and lead them through two small holes in the former to the outside and then solder these to the outside strip, you then solder about 300mm of wire to the other end of the outside strip to be lead inside the mirror cube as per the square lamp above.

Once the soldering is done stick the LED strips to the formers. (in the case of the round formers this involves soldering the inside to the outside strip.)

Step 6: Assemble the Inner Mirror Cube

You should now have 5 assembled LED strips on formers each with 2 x 300mm wires attached. The wires are lead inside via a 3mm hole placed appropriately on the surface of the mirror cube (I cut these holes on the laser but they are easily just drilled).

Glue the former/LED assemblies to the surface of the cube and lead the wires inside.

Step 7: Connect Wires and Final Assembly

Inside the mirror cube there should be 5 sets of positive connections and 5 negatives, gang these together to make one positive and one negative, you could solder but I used a simple electrical connector block. Then connect a 2.1mm x 5.5 mm female jack socket to the connecter block and test the circuit with the 12v supply.

The base consists of 3 layers of 3mm acrylic sheet, I used black in a rounded square shape about 20mm larger than the outer, half mirrored, cube. The top layer has a square cut out just smaller than the inner mirror cube, the middle layer is the same but with a strip cut out of one side to allow the Female jack to be lead to the outside (see photo) and the final, bottom, layer is a blank rounded square that seals the base of the lamp.

The top layer is glued to the inner cube, the second layer is glued onto the top layer and the wire lead out (see photo again) before the final base layer is glued on.

the outer cube is then placed over the inner and glued down onto the base.

The lamp is now complete!

please forgive any omissions and errors, I found these thing much harder to explain than to make.