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.

An illustration of two children, one standing and one resting on its knees, looking at an intricately carved box.

Children Looking at a Large Box

An illustration of two children, one standing and one resting on its knees, looking at an intricately…

"The combination of hexakis-octahedron and cube.

Combination of Hexakis-octahedron and Cube

"The combination of hexakis-octahedron and cube.

The combination of an icositetrahedron and a cube.

Combination of Icositetrahedron and Cube

The combination of an icositetrahedron and a cube.

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.

The combination of tetrakis-hexahedron and cube.

Combination of Tetrakis-hexahedron and Cube

The combination of tetrakis-hexahedron and cube.

The combination of a cube and a triakis-octahedron.

Combination of Triakis-octahedron and cube

The combination of a cube and a triakis-octahedron.

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 regular solid body, with six equal square sides.

Cube

A regular solid body, with six equal square sides.

A cube.

Cube

A cube.

"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

"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…

A cube

Cube

A cube

"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…

An illustration of a cube with the faces shaded.

Cube With Faces Shaded

An illustration of a cube with the faces shaded.

Illustration of 3-dimensional cube with hidden edges shown.

Cube

Illustration of 3-dimensional cube with hidden edges shown.

A cube after additions have been made.

Cube

A cube after additions have been made.

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

Cube and dodecahedron

"A combination of dodecahedron and cube." — 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 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 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 cube (A) has sides of 20 inches in length each, making its solid contents equal 8000 cubic inches. Being added are 3 equal portions 20x20x5, equaling 2000 cubic inches. The sum of these are 6000. You can find the second portion of the problem <a href="../62392/62392_cube_add2.htm">here</a>.

Cube with Additions 1

A cube (A) has sides of 20 inches in length each, making its solid contents equal 8000 cubic inches.…

In order to fill in the spaces from the three 2000 cubic inch additions, four new additions must be added: three 20x5x5 bars equaling 500 cubic inches and a 5x5x5 (125 cubic inches) cube for the corner. You can find the final cube <a href="../62393/62393_cube_add3.htm">here</a>.

Cube with Additions 2

In order to fill in the spaces from the three 2000 cubic inch additions, four new additions must be…

This is the final form of the original 20x20x20 inch or 8000 cubic inch cube with the addition of 7625 cubic inches making it a 25x25x25 inch cube equaling 15,625 cubic inches. You can find the original cube <a href="../62391/62391_cube_add1.htm">here</a>.

Cube with Additions 3

This is the final form of the original 20x20x20 inch or 8000 cubic inch cube with the addition of 7625…

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.

9' by 9' by 9' Cube with diagonals labeled.

Cube 9 by 9 by 9 With Diagonals

9' by 9' by 9' Cube with diagonals labeled.

"A combination of cube, dodecahedron, and tetrahedron." &mdash; Ford, 1912

Cube, dodecahedron and tetrahedron

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

An 1/8 cube.

Eighth Cube

An 1/8 cube.

An 1/4 cube

Fourth Cube

An 1/4 cube

A 1/2 cube

Half Cube

A 1/2 cube

Isometric of a cube with 30&deg;.

Isometric of a Cube

Isometric of a cube with 30°.

Isometric of a cube with circles inscribed on its faces.

Isometric of a Cube With Circles Inscribed

Isometric of a cube with circles inscribed on its faces.

A cube, octahedron, and dodecahedron.

Cube, octahedron and dodecahedron

A cube, octahedron, and dodecahedron.

"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." &mdash; 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…

Cube rotated 30&deg; with vertical plane.

Cube Rotated 30°

Cube rotated 30° with vertical plane.

An illustration of a cube divided into 6 equal pyramids to illustrate how volume can be found.

Cube for Illustrating Volume

An illustration of a cube divided into 6 equal pyramids to illustrate how volume can be found.

"Rollers of cube-cutting machine." &mdash; Encyclopedia Britannica, 1893

Cube-cutting

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

Illustration of 108 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

108 Stacked Congruent Cubes

Illustration of 108 congruent cubes stacked at various heights. A 3-dimensional representation on a…

Illustration of 117 congruent cubes stacked in columns of one, four, and six. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

117 Stacked Congruent Cubes

Illustration of 117 congruent cubes stacked in columns of one, four, and six. A 3-dimensional representation…

Illustration of 128 congruent cubes stacked so they form a rectangular solid that measures 4 by 4 by 8. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

128 Stacked Congruent Cubes

Illustration of 128 congruent cubes stacked so they form a rectangular solid that measures 4 by 4 by…

Illustration of 132 congruent cubes stacked in 22 columns of 6 in the shape of a U. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

132 Stacked Congruent Cubes

Illustration of 132 congruent cubes stacked in 22 columns of 6 in the shape of a U. A 3-dimensional…

Illustration of 154 congruent cubes stacked in columns increasing from one to four. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

154 Stacked Congruent Cubes

Illustration of 154 congruent cubes stacked in columns increasing from one to four. A 3-dimensional…

Illustration of 16 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

16 Stacked Congruent Cubes

Illustration of 16 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 17 congruent cubes stacked in ones and twos in the shape of a V. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

17 Stacked Congruent Cubes

Illustration of 17 congruent cubes stacked in ones and twos in the shape of a V. A 3-dimensional representation…

Illustration of two congruent cubes that are tangent along an edge. A 3-dimensional representation on a 2-dimensional surface.

2 Congruent Cubes

Illustration of two congruent cubes that are tangent along an edge. A 3-dimensional representation on…

Illustration of 20 congruent cubes stacked in twos and threes. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

20 Stacked Congruent Cubes

Illustration of 20 congruent cubes stacked in twos and threes. A 3-dimensional representation on a 2-dimensional…

Illustration of 20 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

20 Stacked Congruent Cubes

Illustration of 20 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 20 congruent cubes stacked at heights increasing from 1 to 4 cubes. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

20 Stacked Congruent Cubes

Illustration of 20 congruent cubes stacked at heights increasing from 1 to 4 cubes. A 3-dimensional…

Illustration of 22 congruent cubes stacked in ones, twos, and threes. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

22 Stacked Congruent Cubes

Illustration of 22 congruent cubes stacked in ones, twos, and threes. A 3-dimensional representation…

Illustration of 22 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

22 Stacked Congruent Cubes

Illustration of 22 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 24 congruent cubes stacked at various heights to resemble steps. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

24 Stacked Congruent Cubes

Illustration of 24 congruent cubes stacked at various heights to resemble steps. A 3-dimensional representation…

Illustration of 256 congruent cubes stacked so they form 4 larger cubes that measures 4 by 4 by 4 each. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

256 Stacked Congruent Cubes

Illustration of 256 congruent cubes stacked so they form 4 larger cubes that measures 4 by 4 by 4 each.…

Illustration of 27 congruent cubes stacked to resemble a larger cube that measures three by three by three cubes. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

27 Stacked Congruent Cubes

Illustration of 27 congruent cubes stacked to resemble a larger cube that measures three by three by…

Illustration of 27 congruent cubes stacked at various heights in the shape of a W. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

27 Stacked Congruent Cubes

Illustration of 27 congruent cubes stacked at various heights in the shape of a W. A 3-dimensional representation…

Illustration of 28 congruent cubes placed in the shape of a square. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

28 Congruent Cubes Placed in the Shape of a Square

Illustration of 28 congruent cubes placed in the shape of a square. A 3-dimensional representation on…

Illustration of 30 congruent cubes stacked in decreasing heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

30 Stacked Congruent Cubes

Illustration of 30 congruent cubes stacked in decreasing heights. A 3-dimensional representation on…