More Pentacube Construction Puzzles

Here are four puzzles each containing 4 pentacubes.

There are four objects to be constructed, "keys", made from assemblies of 20 cubes The objects are related, each has a bottom layer of 16 cubes arranged in a square. A second layer contains 4 additional cubes as follows:

Key_Corner has the four cubes at the corners of the first layer
Key_Diagonal - the four cubes form a diagonal across the first layer
Key_Center has the 4 cubes as a square centered atop the first layer
Key_Edge has the 4 cubes as a square centered at the edge of the first layer
(Note - there are 460 other ways to arrange the 4 cubes atop the first layer.)

Corner_puz_3 constructs both Key Corner and Key_Diagonal
Diagonal_puz_32 constructs both Key Corner and Key_Diagonal
Diagonal_puz_6 constructs Key_Diagonal, Key_Center, and Key Edge
Corner_puz_14 constructs Key_Corner and Key Center

Assemble_pieces.scad contains a description of how the puzzles were created, explains the numbering of the puzzles