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A small cube, marked on its faces with spots from one to six.

Die

A small cube, marked on its faces with spots from one to six.

A regular solid body, with six equal square sides.

Cube

A regular solid body, with six equal square sides.

A cube.

Cube

A cube.

"When a corner or an edge of one form is replaced by a face of another form, the first is said to be trunctuated by the second." — Ford, 1912

Cube trunctuated by octahedron

"When a corner or an edge of one form is replaced by a face of another form, the first is said to be…

"When a corner or an edge of one form is replaced by a face of another form, the first is said to be trunctuated by the second." — Ford, 1912

Octahedron trunctuated by cube

"When a corner or an edge of one form is replaced by a face of another form, the first is said to be…

"A penetration twin, since the two individuals interpenetrate each other." — Ford, 1912

Twinned cubes

"A penetration twin, since the two individuals interpenetrate each other." — Ford, 1912

"A combination of dodecahedron and cube." — Ford, 1912

Cube and dodecahedron

"A combination of dodecahedron and cube." — Ford, 1912

A cube, octahedron, and dodecahedron.

Cube, octahedron and dodecahedron

A cube, octahedron, and dodecahedron.

"A cube with its edges beveled by the faces of a tetrahexahedron." — Ford, 1912

Cube and tetrahexahedron

"A cube with its edges beveled by the faces of a tetrahexahedron." — Ford, 1912

"A combination of cube and trapezohedron." — Ford, 1912

Cube and trapezohedron

"A combination of cube and trapezohedron." — Ford, 1912

"A combination of cube and hexoctahedron." — Ford, 1912

Cube and hexoctahedron

"A combination of cube and hexoctahedron." — Ford, 1912

"A combination of cube and pyritohedron, in which it will be noted that the faces of the pyritohedron trunctuate unsymmetrically the edges of the cube." — Ford, 1912

Cube and pyritohedron

"A combination of cube and pyritohedron, in which it will be noted that the faces of the pyritohedron…

"A cube trunctuated with pyritohedron and octahedron." — Ford, 1912

Pyritohedron, cube, and octahedron

"A cube trunctuated with pyritohedron and octahedron." — Ford, 1912

"A combination of cube and diploid." — Ford, 1912

Diploid and cube

"A combination of cube and diploid." — Ford, 1912

"A combination of cube and tetrahedron. It will be noted that the tetrahedron faces truncate the alternate corners of the cube, or that the cube faces truncate the edges o a tetrahedron." — Ford, 1912

Cube and tetrahedron

"A combination of cube and tetrahedron. It will be noted that the tetrahedron faces truncate the alternate…

"A combination of cube and tetrahedron. It will be noted that the tetrahedron faces truncate the alternate corners of the cube, or that the cube faces truncate the edges o a tetrahedron." — Ford, 1912

Tetrahedron and cube

"A combination of cube and tetrahedron. It will be noted that the tetrahedron faces truncate the alternate…

"A combination of cube, dodecahedron, and tetrahedron." — Ford, 1912

Cube, dodecahedron and tetrahedron

"A combination of cube, dodecahedron, and tetrahedron." — Ford, 1912

"A regular hexahedron: a solid figure bounded by 6 equal squares." — Williams, 1889

Cube

"A regular hexahedron: a solid figure bounded by 6 equal squares." — Williams, 1889

A regular body with six square faces; a rectangular parallelopiped, having all its edges equal.

Cube

A regular body with six square faces; a rectangular parallelopiped, having all its edges equal.

A solid with fourteen faces formed by cutting off the corners of a cube parallel to the coxial octahedron far enough to leave the original faces squares, while adding eight triangular faces at the truncations.

Cuboctahedron

A solid with fourteen faces formed by cutting off the corners of a cube parallel to the coxial octahedron…

Insects working as a team to collect ice cubes from a well.

Insect Ice

Insects working as a team to collect ice cubes from a well.

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which belongs a number of forms having some property in common. In order to classify these different crystals, the existence of certain lines within the crystal, called axes, is assumed, around which the form can be symmetrically build up. These axes are assumed to intersect in the center of the crystal, and to pass through from one side to the other." — Hallock, 1905

Cube

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which…

"One of the most important of astronomical instruments, consists of a telescope fixed to a horizontal axis, so as to revolve in the plane of the meridian, and is employed, as its name denotes, in the observation of the meridian transits of the heavenly bodies. The axis, which is the most important part of the instrument, and thus demands the utmost care in its construction, consists of a hollow sphere or cube, to opposite sides of which are tightly fastened the bases of two cones in whose apices the pivots are screwed; the sphere or cube is pierced for the admission of the telescope, which is firmly soldered at right angles to the axis." — Chambers, 1881

Transit Instrument

"One of the most important of astronomical instruments, consists of a telescope fixed to a horizontal…

"Rollers of cube-cutting machine." — Encyclopedia Britannica, 1893

Cube-cutting

"Rollers of cube-cutting machine." — Encyclopedia Britannica, 1893

A pentagonal dodecahedron. A solid contained by twelve pentagons.

Pyritohedron

A pentagonal dodecahedron. A solid contained by twelve pentagons.

A solid bound by six rhombic planes.

Rhombohedron

A solid bound by six rhombic planes.

A solid bound by six rhombic planes.

Rhombohedron

A solid bound by six rhombic planes.

A solid bound by six rhombic planes.

Rhombohedron

A solid bound by six rhombic planes.

"In this the four lateral planes are rectangular and equal; they may be either oblong or square; in the latter case the form is the cube." —The Encyclopedia Britannica, 1903

Primitive Crystal

"In this the four lateral planes are rectangular and equal; they may be either oblong or square; in…

"If the base is a square and the prism stands erect—that is, if its sides or lateral planes, as they are called, are perpendicular to the base—the form is termed a right square prism." —The Encyclopedia Britannica, 1903

Primitive Crystal

"If the base is a square and the prism stands erect—that is, if its sides or lateral planes, as…

"When the base is a rectangle instead of a square, the form is a right rectangular prism." —The Encyclopedia Britannica, 1903

Primitive Crystal

"When the base is a rectangle instead of a square, the form is a right rectangular prism." —The…

"When the base is a rhombus, and the prism stands erect, the form is a right rhombic prism." —The Encyclopedia Britannica, 1903

Primitive Crystal

"When the base is a rhombus, and the prism stands erect, the form is a right rhombic prism." —The…

"When the base is a rhomboid, and the prism stands erect, it is only the opposite laeral faces that can be equal. The form is called a right rhomboidal prism." —The Encyclopedia Britannica, 1903

Primitive Crystal

"When the base is a rhomboid, and the prism stands erect, it is only the opposite laeral faces that…

A cube

Cube

A cube

A 1/2 cube

Half Cube

A 1/2 cube

An 1/8 cube.

Eighth Cube

An 1/8 cube.

An 1/4 cube

Fourth Cube

An 1/4 cube

This object is a cube, having therefore all its faces of equal dimensions; and as both sides recede, "angular perspective" is employed. The point of sight, horizontal line, and point of station, having been fixed upon, the line A is first to be drawn, touching the bottom of the nearest corner, and is for the geometrical scale or height of the cube, which, in this instance, will be called twelve feet; that is, twelve feet must be marked on the scale from the corner on either side. 1) The ground line of the square, taken from the centre of the geometrical scale line to the horizontal line; by its junction with which is determined the vanishing point or that side. 2) A line drawn from the above vanishing point to the point of station. 3) A line drawn at right angles at the point of station to the line 2, as far as the horizontal line, its intersection with which will give the correct vanishing point to the other side. 4) The ground line of the cube running to the last vanishing point. 5) The nearest corner of the cube, twelve feet in height, being equal to the width. The points of measurement are next to be ascertained, and to be marked in the usual way; and the lines B drawn from the ends of the geometrical scale towards the point of measurement give the perspective width or depth of both sides. This is found at their cutting of the ground lines 1 and 4. The line 6 represents the top line of one side of the cube, and runs from the nearest corner to the vanishing point. 7) The other top line; and it is drawn to the other vanishing point. 8) The far corner line raised vertically from the crossing of the lines B and 1. 9) The other corner line raised vertically from the intersection of the lines B and 4. The lines 1, 4, 5, 6, 7, 8, 9, being strengthened, the figure is complete.

Angular Perspective

This object is a cube, having therefore all its faces of equal dimensions; and as both sides recede,…

This cube has four additional cubes of equal dimensions. This is effected by first drawing the cube in the order and then finding the centre of the upright line 5, that being the nearest corner line of this first cube. The centre being found at 10, take the line 10 to the vanishing point for that side of the cube; this will give the centres of all the other upright lines of that side of all the added cubes. The line 11 is drawn from the top of the corner line 5, through the intersection of 8 and 10, until it meets the ground line 1, at its junction with which the upright line is raised for the far corner line 12 of the second cube. The three other cubes are described precisely in the same manner, being found by the diagonal lines traversing each pair of the cubes, through the intersection of the centre line 10, with each perpendicular line raised from the meeting of the previous diagonal line with the ground line 1. It will be perceived that a further distance of twelve feet is added to one side of the geometrical scale, and marked A. This is done merely to prove the correctness of the first diagonal line 11, passing through the centre line 10, to determine the perspective depth of the second cube. For if a line be taken from the end of the geometrical scale A to the point of measurement on the horizontal line, it will be found to meet the ground line 1 at exactly the same point; thus proving the truth of both modes of drawing. The former mode, however, is more convenient where a number of cubes are to be drawn; as the geometrical scale might extend far beyond the limits of the paper, and consequently give much more trouble.

Angular Perspective

This cube has four additional cubes of equal dimensions. This is effected by first drawing the cube…

This figure differs from the others because they are solid cubes. Further, the geometrical scale is used for the two cubes, because, being only two, it will be found in this way that fewer lines will be necessary, leaving the figure less intricate and confused. The two frnt sides of the cubes are produced in the same way as far as line 10, which is the farthest corner line of the second cube. 11) The line is drawn from the extremity of 10 to the vanishing point of 7, the two lines being really parallel. 12) Is drawn from the top of 9 to the vanishing point of line 6, these also being parallel. 13) Is drawn from the top of the upright centre line 8, to the vanishing point of 11 and 7, these being all really parallel to each other. 14) Is the far ground line taken from the lower extremity of 9 to the vanishing point of 1, these lines being also parallel. 15 and 16) Are lines drawn from the corner end of 10 and 8 to the vanishing point of 4, the three lines being really parallel. 17 and 18) Are upright lines raised at the intersection of the lines 16 and 15, with the ground line 14, being the far corners of the cubes; they respectively will meet the intersections of lines 11 and 13 with 12. These lines will complete the figure.

Angular Perspective

This figure differs from the others because they are solid cubes. Further, the geometrical scale is…

A cube crystal of Boracite

Boracite Crystal

A cube crystal of Boracite

Squares that have many more summations than just rows, columns, and diagonals. Frost extended this idea to cubes, where various sections have the same singular properties.

Nasik Cube

Squares that have many more summations than just rows, columns, and diagonals. Frost extended this idea…

"Shear is a particular form of strain produced by causing plane layers of a material to slide parallel to one another through spaces proportional to their distances from a fixed parallel plane"—Finley, 1917

Shear

"Shear is a particular form of strain produced by causing plane layers of a material to slide parallel…

Diagram showing all of the different axes of symmetry of a cube.

Axes of Symmetry of a Cube

Diagram showing all of the different axes of symmetry of a cube.

Represents the combination of an octrahedron and a cube, with the cube faces predominate.

Cube in Combination with Octahedron

Represents the combination of an octrahedron and a cube, with the cube faces predominate.

Represents the combination of a cube and an octahedron, with both faces being equal.

Cubo-octahedron

Represents the combination of a cube and an octahedron, with both faces being equal.

Represents the combination of an octahedron and a cube, with the octahedron predominate.

Octahedron in Combination with Cube

Represents the combination of an octahedron and a cube, with the octahedron predominate.

"A drawing of a crystal showing a combination of the cube, octahedron and rhombic dodecahedron is shown, in which the faces are lettered the same as the corresponding poles in the projection." -The Encyclopedia Britannica 1910

Clinographic Drawing of a Cubic Crystal

"A drawing of a crystal showing a combination of the cube, octahedron and rhombic dodecahedron is shown,…

The combination of a cube and a triakis-octahedron.

Combination of Triakis-octahedron and cube

The combination of a cube and a triakis-octahedron.

The combination of an icositetrahedron and a cube.

Combination of Icositetrahedron and Cube

The combination of an icositetrahedron and a cube.

The combination of tetrakis-hexahedron and cube.

Combination of Tetrakis-hexahedron and Cube

The combination of tetrakis-hexahedron and cube.

"The combination of hexakis-octahedron and cube.

Combination of Hexakis-octahedron and Cube

"The combination of hexakis-octahedron and cube.

Represents one way a tetrahedron and a cube might combine.

Combination of Tetrahedron and Cube

Represents one way a tetrahedron and a cube might combine.

A tetrahedral combination.

Combination of Tetrahedron, Cube and Rhombic Dodecahedron

A tetrahedral combination.

Represents a combination of a pentagonal dodecahedron and cube, and are common in pyrites.

Combination of Pentagonal Dodecahedron and Cube

Represents a combination of a pentagonal dodecahedron and cube, and are common in pyrites.

Represents the combination of pentagonal dodecahedron, cube, and octahedron.

Combination of Pentagonal Dodecahedron, Cube and Octahedron

Represents the combination of pentagonal dodecahedron, cube, and octahedron.

Rectangular prism/solid.

Rectangular Prism

Rectangular prism/solid.

"Here one cube may be brought into the position of the other by a rotation of 180 degrees about a traid axis, or by reflection across the octrahedral plane which is perpendicular to this axis." -The Encyclopedia Britannica 1910

Interpenetrating Twinned Cubes

"Here one cube may be brought into the position of the other by a rotation of 180 degrees about a traid…

"It is evident that, when a solid is immersed in a fluid, it will displace exactly its own volume of the fluid. Immerse a solid cube one centimeter on each edge in water, so that its upper face shall be level and one centimeter below the surface of the liquid, as shown. The lateral pressures upon any two opposite vertical surfaces of the cube, as a and b, are clearly equal and opposite." -Avery 1895

Archimedies Principle

"It is evident that, when a solid is immersed in a fluid, it will displace exactly its own volume of…

"A cube is a prism whose faces are ends are squares. All the faces of a cube are equal." —Hallock 1905

Cube

"A cube is a prism whose faces are ends are squares. All the faces of a cube are equal." —Hallock…