On the Interpretation of Facets & Logic

Really throwing a curve ball on this one, huh?

The module presents itself one of 12 different polyhedrons with buttons on each of its faces. Each button has a black and white image resulted from 2 images XORed on top of each other, via transparency. Selecting the border surrounding the polyhedron will rotate the polyhedron to get a better view.

This table has names of each polyhedron that can be displayed.

Polyhedron	Vertices	Faces
Deltoidal Icositetrahedron	26	24
Disphenocingulum	16	24
Gyroelongated Triangular Bicupola	18	26
Icosidodecahedron	30	32
Pentagonal Icositetrahedron	38	24
Rhombic Triacontahedron	32	30
Rhombicuboctahedron	24	26
Snub Square Antiprism	16	26
Tetrakis Hexahedron	14	24
Triakis Octahedron	14	24
Triaugmented Dodecahedron	23	24
Truncated Icosahedron	60	32

Page 2 contains all possible conditions that can show up on the module. The right side of the table corresponds to the groupings of each condition. Pages 3 to 6 will contain ALL 252 combinations that show up on the module, with pages 5 and 6 showing inverted variants of pages 3 and 4.

Each button has an initial boolean state determined by its initial condition, and a final state which is determined by its final condition and adjacent faces' initial states. Buttons that must be pressed have a final state that is true. Symbols that are inverted, ONLY invert the initial boolean state from the initial conditions, NOT the final boolean states from the final conditions.

Initial conditions are lettered from A; final conditions are numbered from 1. Both are separated by a line to differentiate between the two.

A	On Triangle	FC
B	On Quadrilateral	FC
C	On Pentagon	FC
D	Adjacent to Triangle	AF
E	Adjacent to Quadrilateral	AF
F	Adjacent to Pentagon	AF
G	Adjacent to two or more Distinct Faces	AF
H	Adjacent to FC condition	GA
I	Adjacent to AF condition	GA
J	Adjacent to GA condition	GA
K	Adjacent to ED condition	GA
L	Adjacent to more than two Distinct Groups	GA
M	Fewer than 25 Faces	ED
N	Fewer than 25 Vertices	ED
O	More Faces than Vertices	ED
P	Adjacent to only one Distinct Polygon	ED
Q	All Serial Number letters are contained in the Name of the Polyhedron	ED
R	All letters in indicators are contained in the Name of the Polyhedron	ED
1	Adjacent to Odd amount of True initial	-
2	Adjacent to Even amount of True initial	-
3	Adjacent to Odd amount of False initial	-
4	Adjacent to Even amount of False initial	-
5	Adjacent to More True initial than False initial	-
6	Adjacent to More False initial than True initial	-
7	Adjacent to Exactly three True initial or three False initial	-

Normal Symbols A - I

	1	2	3	4	5	6	7
A
B
C
D
E
F
G
H
I

Normal Symbols J - R

	1	2	3	4	5	6	7
J
K
L
M
N
O
P
Q
R

Inverted Symbols A - I

	1	2	3	4	5	6	7
A
B
C
D
E
F
G
H
I

Inverted Symbols J - R

	1	2	3	4	5	6	7
J
K
L
M
N
O
P
Q
R