Complete list of constructible octominoid shapes

Shapes and configurations not listed here are proved not to be constructible by computing the two invariants.
For all shapes the indication in square brackets indicates if it is nonsymmetric ([Uc]) or if it is symmetric ([Sx]) in which case x indicates the order of the symmetry group.
A letter c if present indicates that the shape is chiral.
Click on an image to obtain detailed information on corresponding configurations.
Terminology used in the building instructions
Go to restricted list of symmetric shapes
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box 0x2x4:

(+8)
[S8]
box 0x3x3:

(+8)
[S4]
box 1x2x2:

(+8)
[S2] 2c [S2] 2c [S4] 2c [S2] 2c [S2] 2c [Uc] 2c [Uc] 2c [S2] [S2] 2c [S4] [S16]

(+7)
[Uc] [Uc] [S2]

(+6)
[S2] [S2] 4c [S2] 2c [S2] 2c [S2] 4c [Uc] 2c [S2] 4c [Uc] 4c [Uc] [Uc] 2c [Uc] 4c [Uc] 2c [Uc] 2c [Uc] [Uc] [Uc] 2c [Uc] 2c [S2] 2c [Uc] [S2] 2c [Uc] 2c [S2c] [Uc] [Uc] [Uc] [Uc] 2c [Uc] [Uc] [Uc] 2c [S2] 2c [S2] 2c [Uc] 2c [S2] 2c [Uc] 2c [S4] [S2] 2c [S2] 2c [S4]

(+5)
[Uc] 2c [Uc] 2c [Uc] [Uc] [Uc] 2c [Uc] [Uc] [Uc] 4c [Uc] [Uc] 2c [Uc] [Uc] 2c [Uc] [Uc] [Uc] 2c [Uc] 2c [Uc] 2c [Uc] [Uc] [Uc] [Uc] [Uc] 2c [Uc] [Uc] [Uc] [Uc] 2c [Uc] 4c [Uc] [Uc] [Uc] [Uc] [Uc] 2c

(+4)
[Uc] [Uc] 2c [S2c] [S2] [Uc] [Uc] [Uc] 2c [Uc] [S4] [S2] 2c [Uc] 2c [Uc] 2c [S2] 2c [S4] 3c [Uc] 2c [Uc] [S2] [S8]
box 2x2x2:

(+8)
[S4] 2c

(+6)
[Uc] [S2] 2c [S2] 2c

(+5)
[Uc] [Uc]

(+4)
[S4] 2c [Uc] 2c [Uc] [Uc] 2c [S2] 2c [S2] 2c [Uc] [S2] 2c [S2] 2c [S2] 2c [S2c] [S4] 2c [S4]

(+3)
[Uc] [Uc] [Uc] 2c [Uc] 2c [Uc] 2c [Uc] [Uc] [Uc] [Uc] [Uc] 2c [Uc] [Uc] [Uc] [Uc]

(+2)
[Uc] [Uc] 2c [Uc] 2c [Uc] [S2] [Uc] 2c [Uc] 2c [Uc] 2c [Uc] 2c [Uc] 2c [Uc] 2c [S2] 4c [Uc] 2c [S2] 2c [S2] 2c [Uc] [S2] 2c [Uc] [Uc] [Uc] 2c [Uc] [S2] 2c [Uc] [S2] 2c [Uc] [Uc] [Uc] [Uc] 2c [Uc] 2c [S2] 2c [S2] 2c [S2] 2c [S2c]

(+0)
[Uc] 8c [S4] 2c [Uc] 4c [S2] 10c [S2c] [Uc] 6c [S16] 4c [S2c] 8c [Uc] 4c [S4] 4c [S8] 2c
box 1x2x3:

(+8)
[Uc] 2c [S2] 2c [Uc] 2c

(+6)
[S2] 4c [S2] [S2] [Uc] [Uc] [S2] 2c [S2]

(+5)
[Uc] 2c [Uc] 2c [Uc] 2c [Uc] [Uc] 2c [Uc] 2c [Uc] [Uc] 2c [Uc] 2c

(+4)
[Uc] 4c [Uc] [S2] [Uc] [S2] [Uc] [Uc] 2c [Uc] [Uc] [Uc] 2c [Uc] [S2] [Uc] [S2] 2c

(+3)
[Uc] 2c [Uc] 2c [S2] [S2] [Uc]

(+2)
[S2]

(+1)
[S4]
box 1x1x3:

(+8)
[Uc] 2c [S2] 2c [S2c] 2c [S4] [S8] [S4]

(+6)
[Uc] [Uc] [S2] [Uc] [Uc] [Uc] [Uc] [Uc] [S2c]
box 2x2x3:

(+0)
[Uc] 2c [S2] 2c [Uc] 2c [Uc] [Uc] 2c [S2] 2c [Uc] [Uc] [Uc] [Uc] [S2] 2c [S2c] [Uc] 2c [S2c] [S4]
box 1x1x4:

(+8)
[S4] 2c

(+6)
[S2] 2c [S4]
box 1x1x2:

(+8)
[S4] 4c [S16] 3c [S4] 2c [S4] 2c

(+7)
[Uc] [S2] 2c [S2] 4c [Uc] [S2]
box 1x3x3:

(+0)
[S4] [S8]

Total of 265 shapes (460 configurations)
A detailed page including a list of configurations per shape is available