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Cube is a 1997 Canadian independent science fiction horror film directed and co-written by Vincenzo Natali.[8] A product of the Canadian Film Centre's First Feature Project,[9] Nicole de Boer, Nicky Guadagni, David Hewlett, Andrew Miller, Julian Richings, Wayne Robson, and Maurice Dean Wint star as individuals trapped in a bizarre and deadly labyrinth of cube-shaped rooms.

Cube gained notoriety and a cult following for its surreal and Kafkaesque setting in industrial, cube-shaped rooms. It received generally positive reviews and led to a series of films. An American remake, currently on hold, was in development at Lionsgate in 2015,[10] though current development is unknown. A Japanese remake was released in 2021.

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A man named Alderson awakens in a mysterious cube-shaped room. He enters another red-colored room, but a thin wire mesh slices him into cubes, gorily killing him before retracting to its original position.

Quentin believes each person was chosen specifically to be there. Leaven hypothesizes that rooms whose plates contain prime numbers are trapped. While exploring, they encounter a seemingly mentally handicapped man named Kazan. Holloway, a free clinic doctor, insists they bring him along, much to the annoyance of Quentin. After Quentin injures his leg in a trapped room Leaven deemed safe, tension rises among the group, as well as the mystery of the maze's purpose. The nihilistic Worth admits to Quentin he helped construct the cube, designing its outer shell, and claims it was for a shady bureaucracy of some kind. He guesses that the original purpose has been long-since forgotten, and they have only been placed inside to simply just put it to use.

Quentin, becoming more unhinged, persuades Leaven to abandon Kazan and Worth. He tries to sexually assault her, but Worth attacks him. Quentin counters savagely, dropping him into the room below. Worth starts laughing hysterically, realizing they are in the same room Rennes died, indicating they have been traveling in circles. Quentin is horrified, but Worth finds the room where Rennes died in has now moved to the edge of the maze. Leaven deduces that traps are not tagged by prime numbers, but by powers of prime numbers. Kazan is revealed as an autistic savant[11] who can mentally calculate prime factorizations. With this newfound knowledge, Leaven guides the group to the edge cube, using Kazan's calculations. Worth then traps Quentin in the door, letting Leaven and Kazan escape from him. When Quentin finds them, he attempts to harm them, before Worth opens the hatch under him from the room below. The others travel to the bridge room where they open the exit hatch, seeing a bright light.

As Leaven attempts to persuade the guilt-stricken Worth, who no longer wishes to escape, Quentin reappears and impales her with a hatch lever. Worth angrily attacks Quentin. Quentin heavily wounds him in the struggle and pursues Kazan to the other side. Worth grabs Quentin's legs, pinning him in between the hatch. The cubes move, splitting him in half. Worth, bleeding badly, crawls to Leaven who lays near unmoving to stay by her side. Kazan wanders out into the bright light, his fate left unknown.

Director Vincenzo Natali did not have confidence in financing a film. He cost-reduced his pitch with a single set reused as many, with the actors moving around a virtual maze.[15] As the most expensive element, a set with a cube and a half was built off the floor, to allow the surroundings to be lit from behind all walls of the cube.[16] In 1990, Natali had had the idea to make a film "set entirely in hell", but in 1994 while working as a storyboard artist's assistant at Canada's Nelvana animation studio, he completed the first script for Cube. The initial draft had a more comedic tone, surreal images, a cannibal, edible moss growing on the walls, and a monster that roamed the Cube. Roommate and childhood filmmaking partner Andre Bijelic helped Natali strip the central idea to its essence of people avoiding deadly traps in a maze. Scenes outside the cube were deleted, and the identity of the victims changed. In some drafts, they were accountants and in others criminals, with the implication that their banishment to the Cube was part of a penal sentence. One of the most important dramatic changes was the removal of food and water for a more urgent escape.[17]

The set's warehouse was near a train line, and its noise was incorporated into the film as that of the cubes moving.[22] To change the look of each room, some scenes were shot with wide lens, and others are long lens and lit with different colors, for the illusion of traversing a maze.[14] Nicole de Boer said that the white room was more comforting to actors at the start of a day's filming, compared to the red room which induced psychological effects on the cast during several hours in the confined space.[23]

The Cube was conceived by mathematician David W. Pravica, who was the math consultant.[24] It consists of an outer cubical shell or sarcophagus, and the inner cube rooms. Each side of the outer shell is 434 feet (132 m) long. The inner cube consists of 263 = 17,576 cubical rooms (minus an unknown number of rooms to allow for movement), each having a side length of 15.5 feet (4.7 m). A space of 15.5 feet (4.7 m) is between the inner cube and the outer shell. Each room is labelled with three identification numbers such as "517 478 565". These numbers encode the starting coordinates of the room, and the X, Y, and Z coordinates are the sums of the digits of the first, second, and third number, respectively. The numbers also determine the movement of the room. The subsequent positions are obtained by cyclically subtracting the digits from one another, and the resulting numbers are then successively added to the starting numbers.[25]

Only one cube set was actually built, with each of its sides measuring 14 feet (4.3 m) in length, with only one working door that could actually support the weight of the actors. The colour of the room was changed by sliding panels.[26] This time-consuming procedure determined that the film was not shot in sequence, and all shots taking place in rooms of a specific color were shot separately. Six colors of rooms were intended to match the recurring theme of six throughout the film; five sets of gel panels, plus pure white. However, the budget did not stretch to the sixth gel panel, and so the film has only five room colors. Another partial cube was made for shots requiring the point of view of standing in one room and looking into another.[27]

Bob Graham of the San Francisco Chronicle was highly critical: "If writer-director Vincenzo Natali, storyboard artist for Keanu Reeves's Johnny Mnemonic, were as comfortable with dialogue and dramatizing characters as he is with images, this first feature of his might have worked better".[34] Nick Schager from Slant Magazine rated the film three out of five stars, noting that, its intriguing premise and initially chilling mood were undone by threadbare characterizations, and lack of a satisfying explanation for the cube's existence. He concluded the film "winds up going nowhere fast".[35]

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In geometry, a cube[a] is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meeting at each vertex. Viewed from a corner, it is a hexagon and its net is usually depicted as a cross.[1]

The cube is also a square parallelepiped, an equilateral cuboid, a right rhombohedron, and a 3-zonohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations.

The cube is dual to the octahedron. It has cubical or octahedral symmetry, and is the only convex polyhedron whose faces are all squares. Its generalization for higher-dimensional spaces is called a hypercube.

The cube can also be represented as a spherical tiling, and projected onto the plane via a stereographic projection. This projection is conformal, preserving angles but not areas or lengths. Straight lines on the sphere are projected as circular arcs on the plane.

This configuration matrix represents the cube. The rows and columns correspond to vertices, edges, and faces. The diagonal numbers say how many of each element occur in the whole cube. The nondiagonal numbers say how many of the column's element occur in or at the row's element.[2] For example, the 2 in the first column of the middle row indicates that there are 2 vertices in (i.e., at the extremes of) each edge; the 3 in the middle column of the first row indicates that 3 edges meet at each vertex.

Doubling the cube, or the Delian problem, was the problem posed by ancient Greek mathematicians of using only a compass and straightedge to start with the length of the edge of a given cube and to construct the length of the edge of a cube with twice the volume of the original cube. They were unable to solve this problem, which in 1837 Pierre Wantzel proved it to be impossible because the cube root of 2 is not a constructible number.

The cube has four classes of symmetry, which can be represented by vertex-transitive coloring the faces. The highest octahedral symmetry Oh has all the faces the same color. The dihedral symmetry D4h comes from the cube being a solid, with all the six sides being different colors. The prismatic subsets D2d has the same coloring as the previous one and D2h has alternating colors for its sides for a total of three colors, paired by opposite sides. Each symmetry form has a different Wythoff symbol.

A cube has eleven nets: that is, there are eleven ways to flatten a hollow cube by cutting seven edges.[4] To color the cube so that no two adjacent faces have the same color, one would need at least three colors. 2351a5e196