If you are going to put this in an algorithm. You need to rember that you also need every 1, 2, 3, and 4 layer shapes.

I calculated 1,748,908,916,031,341,158,465,536 shapes

Whoops, it's actually 1,912,880,283,810,558,911,801,524 shapes.

Dang

Quick maths: a lot

1.912880283810558911801524×10²⁴

32^256 the value is approximately 2,0815864389328798163850480654728x10^385

There is some shapes could have fully empty lower layers which means you will never build them in game but they are truly exist. Acturally you just simply multiply several numbers then you get the total. 4layers * 4quandrens * ( 8colors * 4typeofshape + 1empty ) = 528. Not too much, huh?

Each quadrant is either a certain shape with a certain color or empty, so we can define q as (8*4)+1, which is 33.

There are 4 quadrants in each layer, but they can't be fully empty, so we can define l as q^4-1, which is 1,185,920.

There can be 1-4 layers in each shape, so we can define s as l+l^2+l^3+l^4, which totals to... *drumroll* 1.9779801978×10^24! That's approximately 1,977,980,197,800,000,000,000,000 (1 septillion 977 sextillion 980 quintillion 197 quadrillion 800 trillion)!

That's right! It isn't 1.748908916*10^27, nor is it a whoppin' 2.0815864389*10^385! It's somewhere in between, as 1 septillion 977 sextillion.

I made a mistake.

I said 1.9779801978×10^24 was "somewhere in between" 1.748908916*10^27 and 2.0815864389*10^385, but 1.9779801978×10^24 is LESS than both other numbers!

I'm sorry.