As the title suggest, this dice is constructed using two popular chips widely available almost everywhere. Add some passive components and you are done. You can even build this on a bread board, although a PCB would be better which you can build yourself too.
Press the S1 push switch, Q1 transistor turns on and activates the 555 timer chip which acts as a multi-vibrator here.
When you power up the kit for the first time and press the switch S1, all the LEDs starts glowing, and then in about 7 seconds, finally any one to all seven LEDs glow, in a random fashion. You press S1 once again, another set of LEDs glow in a similar random way.
Although you can construct this on a breadboard or general purpose PCB, but a professionally designed PCB as shown above is highly recommended.