Now I for one like stellated geometry – taking regular solids and adding pointy things is very satisfying:

The pointy things on this solid are rhomboid – so not strictly regular pyramidal but 4-sided none the less.

Designed by  Jeannine Mosely, you can have a go at this by jumping here.

I used 4 types of patterned paper – macaron, chocolate, biscuit and fruit& nut – the resultant sold gave me a sugar craving that has taken ages to subside. Started during an exam supervision, completed today I am quite pleased with this. The locking mechanism is pure evil, particularly when the 3rd and 4th ring are interwoven.