529:. A 5×4 rectangle with a checkerboard pattern has 20 squares, containing 10 light squares and 10 dark squares, but a complete set of free tetrominoes has either 11 dark squares and 9 light squares, or 11 light squares and 9 dark squares. This is due to the T tetromino having either 3 dark squares and one light square, or 3 light squares and one dark square, while all other tetrominoes each have 2 dark squares and 2 light squares. Similarly, a 7×4 rectangle has 28 squares, containing 14 squares of each shade, but the set of one-sided tetrominoes has either 15 dark squares and 13 light squares, or 15 light squares and 13 dark squares. By extension, any odd number of sets for either type cannot fit in a rectangle. Additionally, the 19 fixed tetrominoes cannot fit in a 4×19 rectangle. This was discovered by exhausting all possibilities in a computer search.
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i i i t l l l 3.) 2×4×4 box filled with one set of all tetrominoes: F T T T F Z Z B F F T B Z Z B B O O L D L L L D O O D D I I I I 4.) 2×2×8 box filled with one set of all tetrominoes: D Z Z L O T T T D L L L O B F F D D Z Z O B T F I I I I O B B F 5.) 2×2×7 box filled with tetrominoes, with mirror-image pieces removed: L L L Z Z B B L C O O Z Z B C I I I I T B C C O O T T T
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227:. There are seven distinct one-sided tetrominoes. These tetrominoes are named by the letter of the alphabet they most closely resemble. The "I", "O", and "T" tetrominoes have reflectional symmetry, so it does not matter whether they are considered as free tetrominoes or one-sided tetrominoes. The remaining four tetrominoes, "J", "L", "S", and "Z", exhibit a phenomenon called
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1.) 2×4×5 box filled with two sets of free tetrominoes: Z Z T t I l T T T i L Z Z t I l l l t i L z z t I o o z z i L L O O I o o O O i 2.) 2×2×10 box filled with two sets of free tetrominoes: L L L z z Z Z T O O o o z z Z Z T T T l L I I I I t t t O O o o i
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The tetracubes can be packed into two-layer 3D boxes in several different ways, based on the dimensions of the box and criteria for inclusion. They are shown in both a pictorial diagram and a text diagram. For boxes using two sets of the same pieces, the pictorial diagram depicts each set as a
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by one unit. J and L are the same tetracube, as are S and Z, because one may be rotated around an axis parallel to the tetromino's plane to form the other. Three more tetracubes are possible, all created by placing a unit cube on the bent
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lighter or darker shade of the same color. The text diagram depicts each set as having a capital or lower-case letter. In the text diagram, the top layer is on the left, and the bottom layer is on the right.
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The fixed tetrominoes allow only translation, not rotation or reflection. There are two distinct fixed I-tetrominoes, four J, four L, one O, two S, four T, and two Z, for a total of 19 fixed tetrominoes.
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As free tetrominoes, J is equivalent to L, and S is equivalent to Z, but in two dimensions and without reflections, it is not possible to transform J into L or S into Z.
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One-sided tetrominoes are tetrominoes that may be translated and rotated but not reflected. They are used by, and are overwhelmingly associated with,
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A single set of free tetrominoes or one-sided tetrominoes cannot fit in a rectangle. This can be shown with a proof similar to the
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that turns one into the other. A free tetromino is a free polyomino made from four squares. There are five free tetrominoes.
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Two sets of free or one-sided tetrominoes can fit into a rectangle in different ways, as shown below:
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All 7 one-sided tetrominoes fit a 6×5 rectangle with two holes of the same "checkerboard color".
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Each of the five free tetrominoes has a corresponding tetracube, which is the tetromino
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The one-sided tetrominoes (all 7 shown above) have 15 dark squares and 13 light squares.
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Straight: vertical and horizontal reflection symmetry, and two-fold rotational symmetry
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Square: vertical and horizontal reflection symmetry, and four-fold rotational symmetry
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231:. J and L are reflections of each other, and S and Z are reflections of each other.
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The free tetrominoes (left side of line) have 11 dark squares and 9 light squares.
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94:. The tetrominoes used in the game are specifically the one-sided tetrominoes.
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115:. That is, two free polyominos are the same if there is a combination of
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950:(2nd ed.). Princeton, New Jersey: Princeton University Press.
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Polyominos are formed by joining unit squares along their edges. A
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All three sets of tetrominoes can fit rectangles with holes:
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in 1953 along with other nomenclature related to polyominos.
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53:(i.e. at the edges and not the corners). Tetrominoes, like
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All 19 fixed tetrominoes fit a 11×7 rectangle with a hole.
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Filling a modified rectangle with one set of tetrominoes
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All 5 free tetrominoes fit a 7×3 rectangle with a hole.
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Two sets of one-sided tetrominoes in a 14×4 rectangle
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Two sets of one-sided tetrominoes in a 8×7 rectangle
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One-sided tetrominoes in a rectangle with two holes
130:The free tetrominoes have the following symmetry:
80:A popular use of tetrominoes is in the video game
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658:Two sets of free tetrominoes in a 4×10 rectangle
628:Filling a rectangle with two sets of tetrominoes
646:Two sets of free tetrominoes in a 5×8 rectangle
521:Filling a rectangle with one set of tetrominoes
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694:The name "tetromino" is a combination of the
596:Free tetrominoes in a rectangle with one hole
1602:Tetris Holding, LLC v. Xio Interactive, Inc.
620:Fixed tetrominoes in rectangle with one hole
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973:"Counting polyominoes: yet another attack"
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73:, is a geometric shape composed of four
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559:A 7×4 board has 14 squares each color.
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1540:Ecstasy of Order: The Tetris Masters
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146:S: two-fold rotational symmetry only
140:T: vertical reflection symmetry only
86:created by the Soviet game designer
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1006:, Tetris.com. Retrieved 2014-04-19.
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16:Four squares connected edge-to-edge
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31:A snapshot from a typical game of
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1534:Classic Tetris World Championship
1059:web archive copy of the page here
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111:is a polyomino considered up to
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714:". The name was introduced by
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1614:Tetris: The Games People Play
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722:Filling a box with tetracubes
527:mutilated chessboard argument
1558:Nintendo World Championships
990:10.1016/0012-365X(81)90237-5
971:Redelmeier, D. Hugh (1981).
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61:, are a particular type of
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1166:Magical Tetris Challenge
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831:Z is the same as S in 3D
805:J is the same as L in 3D
77:connected orthogonally.
1145:Tetris & Dr. Mario
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38:
24:
23:The 5 free tetrominoes
1333:Spin-offs and sequels
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217:One-sided tetrominoes
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1588:Blue Planet Software
1138:Tetris Battle Gaiden
1055:The Father of Tetris
977:Discrete Mathematics
751:"straight tetracube"
161:"straight tetromino"
98:Types of tetrominoes
65:. The corresponding
1608:Tetris Online, Inc.
1050:The story of Tetris
1911:Mathematical games
1583:The Tetris Company
1264:Puyo Puyo Tetris 2
942:Golomb, Solomon W.
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765:"square tetracube"
516:Tiling a rectangle
173:"square tetromino"
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1747:Higher dimensions
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1563:Spectrum HoloByte
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1458:Vladimir Pokhilko
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1022:daviddarling.info
716:Solomon W. Golomb
328:Fixed tetrominoes
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1795:Pseudo-polyomino
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1362:Faces...tris III
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1243:Puyo Puyo Tetris
1201:Tetris Evolution
1159:The Grand Master
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819:"skew tetracube"
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103:Free tetrominoes
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1187:The Next Tetris
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1412:Pokémon Tetris
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1180:The New Tetris
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1040:External links
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1004:"About Tetris"
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983:(2): 191–203.
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143:L: no symmetry
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109:free polyomino
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1250:Tetris Effect
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1215:Tetris Splash
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1194:Tetris Worlds
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957:0-691-02444-8
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867:
859:"Right Screw"
853:
839:
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813:
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793:"L-tetracube"
787:
779:"T-tetracube"
773:
759:
745:
736:
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729:
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703:Ancient Greek
701:'four' (from
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197:"L-tetromino"
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185:"T-tetromino"
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1419:Tetris Giant
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1375:
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1353:
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1319:Tetris: Axis
1317:
1310:
1302:
1295:
1288:
1281:
1262:
1255:
1248:
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1234:
1229:Tetris Party
1227:
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1206:
1199:
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1178:
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1150:
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1122:
1114:
1095:
1025:. Retrieved
1021:
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946:
879:
873:"Left Screw"
725:
698:
693:
631:
570:
524:
331:
233:
222:
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129:
117:translations
106:
91:
81:
79:
70:
51:orthogonally
49:, connected
42:
40:
32:
1872:WikiProject
1780:Polydrafter
1754:Polyominoid
1690:Polyominoes
1552:Korobeiniki
1468:Maya Rogers
1463:Henk Rogers
1398:Tetrisphere
1208:Tetris Zone
1152:Tetris Plus
1018:"Polyomino"
947:Polyominoes
125:reflections
69:, called a
59:pentominoes
1895:Categories
1832:Snake cube
1790:Polyiamond
1576:soundtrack
1509:Alex Thach
1405:BreakThru!
1378:(Nintendo)
1284:(Game Boy)
925:References
113:congruence
92:tetriminos
1901:Polyforms
1827:Soma cube
1800:Polystick
1775:Polyabolo
1723:Heptomino
1713:Pentomino
1708:Tetromino
1682:Polyforms
1620:Tetromino
1514:Justin Yu
1304:Tetris DS
1297:3D Tetris
1257:Tetris 99
1173:Tetris 64
919:Pentomino
902:Soma cube
690:Etymology
229:chirality
121:rotations
71:tetracube
63:polyomino
43:tetromino
1842:Hexastix
1759:Polycube
1738:Decomino
1733:Nonomino
1728:Octomino
1718:Hexomino
1639:Category
1391:TetriNET
1376:Tetris 2
1369:Wordtris
1348:Welltris
1341:Blockout
1290:V-Tetris
1274:Handheld
1106:Versions
944:(1994).
896:See also
845:"Branch"
728:extruded
710:), and "
67:polycube
55:dominoes
1848:Tantrix
1837:Tangram
1814:puzzles
1785:Polyhex
1703:Tromino
1527:Related
1477:Players
1027:May 23,
914:Tromino
733:tricube
47:squares
1906:Tetris
1882:Portal
1855:Tetris
1822:Blokus
1768:Others
1698:Domino
1596:effect
1594:Tetris
1571:(film)
1569:Tetris
1436:People
1355:Hatris
1311:Tetris
1282:Tetris
1123:Tetris
1115:Tetris
1097:Tetris
954:
712:domino
707:τετρα-
699:tetra-
696:prefix
224:Tetris
123:, and
83:Tetris
34:Tetris
1810:Games
1546:ELORG
1125:(NES)
75:cubes
1812:and
1313:(EA)
1029:2020
952:ISBN
57:and
985:doi
1897::
1048::
1020:.
981:36
979:.
975:.
933:^
871:F
857:D
843:B
817:S
791:L
777:T
763:O
749:I
735::
119:,
41:A
1674:e
1667:t
1660:v
1554:"
1550:"
1088:e
1081:t
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1061:)
1057:(
1031:.
993:.
987::
960:.
320:Z
308:S
296:L
284:J
272:T
260:O
248:I
37:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
