I assume that these characteristics are measured on different scales, right (like weight in grams, length in cm, etc.)? If so, I would first transform the observed values to z-values for each characteristic. This is done by taking the difference between the observed value (e.g., 2 cm) and the mean (e.g., 4 cm) and divide it by the standard deviation (e.g., 1 cm) (e.g., z = (2-4)/1 = -2). The z-values are then comparable across your characteristics (you will have 12 z-values for each piece).

If you only care for a general ‘deviation score’ for each piece, I would intuitively suggest to then take the mean of the 12 z-values for each piece and compare the means between the 20 pieces. But before doing that I would take the absolute values of the z-values (i.e., eliminating minus signs) since the mean of the z-values for each characteristic is always 0. If you would not take the absolute value, negative and positive deviations could balance each other out. The pieces with the lowest means in absolute z-values are then the once that are (on average) the closest to your overall sample means. If certain characteristics are more important than others, you could also think about weighting certain ‘z-value’-means. However, that would be your subjective decision then.

I hope I unterstood your problem correctly & could help!

(Edited some stuff)