The soma cube was invented by Piet Hein in 1933. It is made from 27 small cubes glued together to form 7 different pieces. 6 have 4 cubes and one has just 3. It is possible to put these pieces together to form a 3x3x3 cube. Apparently the big cube can be made in 240 distinct fashions.
I have taken one such assembly and added dots to some of the small cube faces to make the big cube into a die (plural: dice). It is my belief that this is uniquely one of the 240 different big cubes, but I have no proof. Thus the 7 green pieces shown above can be assembled to look like the (reduced size) blue die.
Each of the 7 pieces has a one letter name (VLTZABP, see pdf). Many other shapes can be made with a set of soma cubes. one such is the "bed", see picture below, which is made as:
Top layer
P.....V
A.....B
A.....B (The dots are not a piece but are free air)
Base layer
PPTLLZV
PTTLZZV
AATLZBB
I have assigned numeric values to each piece (V=1 L=2 T=3 Z=4 A=5 B=6 P=7) and your task is to remake the die and then determine which piece each centre, face, edge and vertex small cube is part of, and hence its value. Should anyone make a valid die and yet, accurately, fail geocheck, it will be because the die assembly is not unique. In which case email me with your assembly solution using the nomenclature demonstrated for the bed: a list of the piece involved for each small cube in the big cube as 3 layers. If your solution works, I will reply with my solution for you to do the evaluation.
There is a pdf which you can print (best onto 160gsm card rather than 80 gsm paper) and cut out (along the double lines) and then fold and sellotape the joins to make the seven pieces. There is also a smaller scale die showing what your final assembly should look like. Each piece has its name (VLTZABP) written on one of its small faces 
.
Alert: You are about to download a file that contains details needed to find this geocache. As the geocache owner, I ensure that this file is safe to download. It has not been checked by Geocaching HQ or by the reviewer for possible malicious content. Download this file at your own risk. pdf
(You can buy soma cube sets made of plastic or of wood. The wooden ones make a nice ornament.)
The cache is hidden at N 51 XX.JKL, W 0 YY.RST
XX = C + F1 + E14 + V135
J = F5 + E26 - V246
K = F2 + E15 - C
L = F3 + E46 - V236
YY = C + F4 + F5 + E24 + E36 + V124 + V456
R = F6 + V356 - E15
S = F2 + E12 - V135
T = F4 + E13 - V246
There is a trophy attached to the outside of the cache for the FTF, who turned out to be natterjacktoad - congratulations.
Please only log a find if you have signed the log. If you haven't, try adding a "write note" instead. Thanks.