#
# list of *symmetric* polyominoids corresponding to
# puzzle configurations having both vanishing invariants
#
#
#    columns meaning
#
# polyominoid:box:num-config:magic27:comment
#
#
#    polyominoid syntax
#
# xyz-xyz-xyz-xyz-xyz-xyz-xyz-xyz[s]
#
# eight groups of 3 digits each.  Each group corresponds to
# a polyominoid square and the 3 digits are the coordinates of
# the square center multiplied by 2: the position of the
# even (doubled) coordinate indicates the direction of the
# normal to the face.
#
#
#    box syntax
#
# AxBxC+D
#
# AxBxC is the size of the bounding box; D is the number of
# tiles that are contained in the boundary of the bounding box
#
#
# num-config: is the number of structurally distinct puzzle
# configurations with vanishing invariants
#
#
# magic27: is a string of the form "magic-x,y" where x,y are
# integers that indicate the row (x) and column (y) in the
# table "magic27.gif" in http://www.mathematische-basteleien.de/magics.htm
#
#-----------------------------------------------------------------------
#
# box 0x2x4
#
011-013-015-017-031-033-035-037s:0x2x4+8:1:-:starting config
#
# box 0x3x3
#
011-013-015-031-033-035-051-053s:0x3x3+8:1:-:solved config
#
# box 1x1x2:
#
011-013-101-103-110-112-121-123s:1x1x2+7:2:magic-6,13
011-013-101-103-110-112-121-211s:1x1x2+7:4:-
011-013-101-110-112-123-211-213s:1x1x2+7:1:-
011-013-101-103-110-114-121-123s:1x1x2+8:4:magic-6,11
011-013-101-103-121-123-211-213s:1x1x2+8:3:magic-6,12
011-013-101-110-114-121-211-213s:1x1x2+8:2:magic-6,10
011-013-101-110-114-123-211-213s:1x1x2+8:2:-
#
# box 1x1x3:
#
011-013-015-101-105-112-114-123s:1x1x3+6:1:magic-5,14
011-013-103-105-112-114-123-213s:1x1x3+6:1:-:cube with two flaps
011-013-015-101-103-105-121-211s:1x1x3+8:2:magic-5,12
011-013-015-101-103-123-125-213s:1x1x3+8:2:-
011-013-015-101-125-211-213-215s:1x1x3+8:1:magic-5,10
011-013-015-110-116-211-213-215s:1x1x3+8:1:magic-5,13
011-013-101-103-123-125-213-215s:1x1x3+8:1:magic-5,11
#
# box 1x1x4:
#
011-013-015-017-103-105-112-116s:1x1x4+6:2:magic-6,9
011-013-015-017-112-116-213-215s:1x1x4+6:1:magic-6,8
011-013-015-017-101-103-105-107s:1x1x4+8:2:magic-6,7
#
# box 1x2x2:
#(magic-2,15 is missing, but unclear)
#
011-013-101-112-123-211-213-312s:1x2x2+4:1:-
011-013-110-112-114-121-123-132s:1x2x2+4:1:magic-2,13
011-013-110-112-211-213-310-312s:1x2x2+4:1:magic-2,12
011-033-101-112-121-123-132-134s:1x2x2+4:2:magic-2,10
011-033-103-112-114-121-123-132s:1x2x2+4:2:magic-2,9
011-101-110-112-121-123-132-211s:1x2x2+4:3:magic-2,11
011-101-112-121-123-132-143-233s:1x2x2+4:1:magic-2,14
011-101-121-211-231-321-341-431s:1x2x2+4:1:magic-2,8
011-013-031-033-101-103-112-132s:1x2x2+6:1:magic-1,15
011-013-031-033-101-103-121-123s:1x2x2+6:4:magic-2,6
011-013-031-033-101-110-112-121s:1x2x2+6:2:magic-2,7
011-013-031-033-101-112-123-134s:1x2x2+6:2:magic-2,4
011-013-031-033-101-112-132-141s:1x2x2+6:4:magic-2,3
011-013-031-033-112-132-211-231s:1x2x2+6:4:magic-2,5
011-013-031-123-132-134-143-233s:1x2x2+6:2:-
011-013-101-103-121-123-231-233s:1x2x2+6:2:magic-1,12
011-013-101-110-112-121-211-231s:1x2x2+6:1:-:cube with 2 flaps
011-013-101-112-114-213-303-314s:1x2x2+6:2:magic-1,17
011-013-101-112-301-312-411-413s:1x2x2+6:2:magic-2,2
011-013-101-114-211-303-312-314s:1x2x2+6:2:magic-1,16
011-013-110-112-310-312-411-413s:1x2x2+6:1:magic-1,14
011-013-110-114-121-123-231-233s:1x2x2+6:2:magic-2,1
011-013-110-114-211-213-301-303s:1x2x2+6:2:magic-1,11
011-013-110-114-211-312-314-413s:1x2x2+6:1:magic-1,13
011-013-031-114-132-211-213-231s:1x2x2+7:1:magic-1,10
011-013-031-033-101-103-110-114s:1x2x2+8:2:magic-1,8
011-013-031-033-101-103-110-130s:1x2x2+8:2:magic-1,5
011-013-031-033-101-103-141-143s:1x2x2+8:2:magic-1,1
011-013-031-033-101-103-211-213s:1x2x2+8:2:magic-1,3
011-013-031-033-101-141-211-231s:1x2x2+8:2:magic-1,7
011-013-031-103-141-213-231-233s:1x2x2+8:1:magic-1,4
011-013-101-114-301-314-411-413s:1x2x2+8:2:magic-1,6
011-013-101-123-301-323-411-413s:1x2x2+8:1:magic-1,9
011-013-110-114-310-314-411-413s:1x2x2+8:1:magic-1,2
#
# box 1x2x3:
#
013-112-114-211-213-215-312-314s:1x2x3+1:1:magic-5,9
011-013-112-114-211-213-215-312s:1x2x3+2:1:-:from 2,12 with flap flipped
011-013-110-114-211-213-215-314s:1x2x3+3:1:magic-5,8
011-013-112-114-215-312-314-413s:1x2x3+3:1:-:from 1,15 with flaps flipped
011-013-015-110-114-211-213-312s:1x2x3+4:1:-:from 1,15 with flaps flipped
011-013-015-121-125-132-134-143s:1x2x3+4:1:magic-5,6
011-013-110-112-310-312-411-512s:1x2x3+4:1:-:from 1,15 with flaps flipped
011-013-114-121-125-132-233-235s:1x2x3+4:2:magic-5,7
011-013-015-031-033-035-112-132s:1x2x3+6:4:magic-5,5
011-013-015-031-033-035-121-123s:1x2x3+6:1:magic-5,4
011-013-015-031-035-132-134-233s:1x2x3+6:1:magic-5,3
011-013-031-033-114-134-215-235s:1x2x3+6:2:magic-5,1
011-013-031-114-132-215-233-235s:1x2x3+6:1:-:from 3,2
011-013-015-031-033-035-110-130s:1x2x3+8:2:magic-5,2
#
# box 1x3x3:
#
112-121-123-125-132-134-143-152s:1x3x3+0:1:-:from 2,12
112-121-123-132-134-143-145-154s:1x3x3+0:1:magic-6,14
#
# box 2x2x2:
#(magic-3,2 and 3,3 are the same)
#(magic-4,15 has 9 tiles!)
#(magic-3,14 3,15 and 4,11 are all the same)
#(magic-4,2 and 4,6 are the same)
#
112-121-123-132-211-213-312-332s:2x2x2+0:2:magic-4,17
112-121-123-132-211-233-312-323s:2x2x2+0:10:magic-4,14
112-121-123-132-211-233-312-332s:2x2x2+0:1:-:4,15 with one less tile
112-121-123-132-312-321-323-332s:2x2x2+0:4:magic-4,12
112-121-123-211-213-231-323-332s:2x2x2+0:8:-:4,15 with one less tile
112-121-123-211-233-321-323-332s:2x2x2+0:4:magic-4,16
112-121-123-231-233-312-321-323s:2x2x2+0:2:magic-4,13
011-013-121-123-132-321-323-332s:2x2x2+2:1:magic-4,3
011-013-121-123-231-233-321-323s:2x2x2+2:4:magic-4,4
011-033-112-121-123-132-312-323s:2x2x2+2:2:magic-4,7
011-101-121-123-132-211-213-312s:2x2x2+2:2:magic-3,13
011-101-121-123-211-213-233-323s:2x2x2+2:2:magic-4,2:also 4,6
011-101-121-132-211-233-312-323s:2x2x2+2:2:magic-4,1
011-101-121-211-231-233-321-323s:2x2x2+2:2:magic-4,10
011-112-121-123-231-233-332-341s:2x2x2+2:2:magic-4,8
011-112-121-123-321-323-332-433s:2x2x2+2:2:magic-3,14:also 3,15 and 4,11
011-112-121-213-231-314-323-332s:2x2x2+2:2:magic-4,9
011-112-121-213-233-321-332-431s:2x2x2+2:1:magic-4,5
011-013-031-033-112-132-312-332s:2x2x2+4:2:magic-3,9
011-013-031-123-132-323-332-433s:2x2x2+4:2:magic-3,10
011-013-101-103-121-211-231-321s:2x2x2+4:2:magic-3,6
011-013-110-112-132-211-231-310s:2x2x2+4:2:magic-3,12
011-013-110-123-132-231-310-321s:2x2x2+4:2:magic-3,7
011-013-110-123-233-310-321-332s:2x2x2+4:2:magic-3,8
011-013-121-123-130-321-323-330s:2x2x2+4:1:-:missing but clearly constructible from the "box-0x3x3"
011-013-121-123-231-233-341-343s:2x2x2+4:2:magic-3,11
011-013-121-123-321-323-431-433s:2x2x2+4:1:magic-3,5
011-013-031-101-103-121-211-301s:2x2x2+6:2:magic-3,4
011-013-031-114-132-233-314-334s:2x2x2+6:2:magic-3,2:also 3,3
011-013-031-033-101-103-301-303s:2x2x2+8:2:magic-3,1
#
# box 2x2x3:
#
112-121-123-125-231-233-235-332s:2x2x3+0:2:magic-6,5
112-121-123-132-312-321-512-521s:2x2x3+0:2:magic-6,1
112-121-213-215-231-323-325-332s:2x2x3+0:2:magic-6,3
112-121-213-215-233-235-321-332s:2x2x3+0:1:magic-6,4
112-121-312-321-323-332-512-523s:2x2x3+0:1:magic-6,6
112-121-312-321-323-332-523-532s:2x2x3+0:1:magic-6,2