Restrictions for some polycubes: Torsten Sillke, 1998-07 Pseudopentacubes with odd x+y+z (mod 3) property: ------------------------------------------------- 000 001 002 010 013 Ref 2 Rot 1 Prop S Order 1 1 1 1 1 1 000 001 010 011 022 Ref 4 Rot 2 Prop S Order 2 1 1 1 1 1 000 001 011 013 022 Ref 2 Rot 1 Prop S Order 1 1 1 1 1 1 000 001 012 020 021 Ref 4 Rot 2 Prop S Order 2 1 1 1 1 1 000 001 012 021 023 Ref 2 Rot 1 Prop S Order 1 1 1 1 1 1 000 001 012 023 024 Ref 4 Rot 2 Prop S Order 2 1 1 1 1 1 000 001 012 122 222 Ref 2 Rot 2 Prop M Order -2 3. 1 1 1 000 002 011 020 022 Ref 16 Rot 8 Prop S Order 8 1 1 1 1 1 000 002 011 121 221 Ref 2 Rot 1 Prop Order 1 3. 1 1 1 000 004 011 013 022 Ref 4 Rot 2 Prop S Order 2 1 1 1 1 1 000 011 013 022 031 Ref 4 Rot 2 Prop S Order 2 1 1 1 1 1 000 011 022 023 032 Ref 4 Rot 2 Prop S Order 2 1 1 1 1 1 001 021 111 210 212 Ref 8 Rot 4 Prop Order 4 1 3:2.3: 1 Pseudotetracubes with even x+y+z (mod 3) property: -------------------------------------------------- 000 001 012 022 Ref 4 Rot 2 Prop S Order 2 1 1 1 1 000 002 011 021 Ref 4 Rot 2 Prop S Order 2 1 1 1 1 000 011 012 023 Ref 4 Rot 2 Prop S Order 2 1 1 1 1 001 010 012 021 Ref 16 Rot 8 Prop S Order 8 1 1 1 1 Pseudopentacubes with x (mod 2) classes are equal (mod 3) property: ------------------------------------------------------------------- This property is valid in 3-dim only for the following pieces. 000 001 002 010 100 Ref 2 Rot 1 Prop Order 1 Test 001 1 2 1 1 000 001 002 010 102 Ref 2 Rot 2 Prop M Order -2 Test 001 1 1 1 2 000 001 002 010 120 Ref 1 Rot 1 Prop M Order -1 Test 001 2. 1 1 1 1 000 001 002 020 110 Ref 1 Rot 1 Prop M Order -1 Test 001 1 1 1 1 1 000 001 002 110 220 Ref 2 Rot 1 Prop Order 1 Test 001 3: 2. 1 1 1 000 001 010 102 202 Ref 1 Rot 1 Prop M Order -1 Test 001 1 1 1 3. 000 001 012 022 102 Ref 2 Rot 1 Prop Order 1 Test 001 1 1 1 1 2. 000 001 012 122 222 Ref 2 Rot 2 Prop M Order -2 Test 101 3. 1 1 1 000 001 020 110 200 Ref 2 Rot 1 Prop Order 1 Test 001 1 1 1 2 000 001 020 110 220 Ref 1 Rot 1 Prop M Order -1 Test 001 1 1 2 1 pentominoes with x (mod 3) classes are equal (mod 2) property: -------------------------------------------------------------- This property is valid in 2-dim only for the following pieces. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -- mailto:Torsten.Sillke@uni-bielefeld.de http://www.mathematik.uni-bielefeld.de/~sillke/