Meet the HyperDiamond! It's the sixth Platonic Solid and it only works in the fourth dimension.

Your best google bet to find more about the hyperdiamond is "24cell".
http://mathworld.wolfram.com/24Cell....

Watch my Royal Institution lecture about 4D shapes:
   • Four Dimensional Maths: Things to See...  

My book: http://makeanddo4d.com/
Maths Gear: http://mathsgear.co.uk/

4D animations made with Stella4D: http://www.software3d.com/Stella.php

MATT PARKER: Standup Mathematician
Website: http://standupmaths.com/

Music by Howard Carter
Design by Simon Wright