Development of an isometric of a cube.

Development of an Isometric of a Cube

Development of an isometric of a cube.

Isometric of a cube with 30°.

Isometric of a Cube

Isometric of a cube with 30°.

Cube rotated 30° with vertical plane.

Cube Rotated 30°

Cube rotated 30° with vertical plane.

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.

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 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 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 33 congruent cubes stacked at various heights in a zigzag pattern. 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.

33 Stacked Congruent Cubes

Illustration of 33 congruent cubes stacked at various heights in a zigzag pattern. A 3-dimensional representation…

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…

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 35 congruent cubes stacked in ones and twos 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.

35 Stacked Congruent Cubes

Illustration of 35 congruent cubes stacked in ones and twos in the shape of a W. A 3-dimensional representation…

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 50 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.

50 Stacked Congruent Cubes

Illustration of 50 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

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 4 congruent cubes stacked in ones and twos. 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.

4 Stacked Congruent Cubes

Illustration of 4 congruent cubes stacked in ones and twos. A 3-dimensional representation on a 2-dimensional…

Illustration of 36 congruent cubes stacked at various heights with outer edges forming 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.

36 Stacked Congruent Cubes

Illustration of 36 congruent cubes stacked at various heights with outer edges forming a square. A 3-dimensional…

Illustration of 56 congruent cubes stacked in twos 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.

56 Stacked Congruent Cubes

Illustration of 56 congruent cubes stacked in twos in the shape of a square. A 3-dimensional representation…

Illustration of 59 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.

59 Stacked Congruent Cubes

Illustration of 59 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

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 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 64 congruent cubes stacked so they form a cube that measures 4 by 4 by 4. 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.

64 Stacked Congruent Cubes

Illustration of 64 congruent cubes stacked so they form a cube that measures 4 by 4 by 4. A 3-dimensional…

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 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 39 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.

39 Stacked Congruent Cubes

Illustration of 39 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 65 congruent cubes stacked at heights increasing from 1 to 5 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.

65 Stacked Congruent Cubes

Illustration of 65 congruent cubes stacked at heights increasing from 1 to 5 cubes. A 3-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 56 congruent cubes stacked in heights of 1, 4, and 5 cubes that form a zigzag pattern. 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.

56 Stacked Congruent Cubes

Illustration of 56 congruent cubes stacked in heights of 1, 4, and 5 cubes that form a zigzag pattern.…

Illustration of 57 congruent cubes stacked in heights of 1 and 5 cubes that form a zigzag pattern. 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.

57 Stacked Congruent Cubes

Illustration of 57 congruent cubes stacked in heights of 1 and 5 cubes that form a zigzag pattern. 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 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 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 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 36 congruent cubes stacked to resemble a 1 by 1 by 1 cube on a 2 by 2 by 2 cube on a 3 by 3 by 3 cube. 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.

36 Stacked Congruent Cubes

Illustration of 36 congruent cubes stacked to resemble a 1 by 1 by 1 cube on a 2 by 2 by 2 cube on a…

Illustration of 35 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.

35 Stacked Congruent Cubes

Illustration of 35 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

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 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 12x12x12 cube of 1,728 cubes.

Cube Area

A 12x12x12 cube of 1,728 cubes.

Illustration of a 5 in. by 3 in. by 4 in. rectangular solid with each cube in the solid representing one cubic inch. This can be used when explaining volume.

Volume Of A Rectangular Solid

Illustration of a 5 in. by 3 in. by 4 in. rectangular solid with each cube in the solid representing…

Various geometric solids, mostly rectangular prisms with a cylinder and a hexagonal prism.

Solids

Various geometric solids, mostly rectangular prisms with a cylinder and a hexagonal prism.

The sector is a hinged rule with scales used for various mathematical calculations.

Sector

The sector is a hinged rule with scales used for various mathematical calculations.

St Mark's Campanile is the bell tower of St Mark's Basilica in Venice, Italy, located in the square (piazza) of the same name. It is a recognizable symbol of the city. The tower is 98.6 meters tall, and stands alone in a corner of St Mark's Square, near the front of the basilica. It has a simple form, the bulk of which is a plain brick shaft, 12 meters on a side and 50 meters tall, above which is the arched belfry, housing five bells. The belfry is topped by a cube, alternate faces of which show walking lions and the female representation of Venice (la Giustizia: Justice). The tower is capped by a pyramidal spire, at the top of which sits a golden weathervane in the form of the archangel Gabriel. The campanile reached its present form in 1514. As it stands today, however, the tower is a reconstruction, completed in 1912 after the collapse of 1902.

St. Mark's Campanile

St Mark's Campanile is the bell tower of St Mark's Basilica in Venice, Italy, located in the square…

Illustration of the development of a rectangular prism. "Assume now that the prism is laid on the drawing board, the surface A face down, and the paper covering removed by turning the prism over and over, the paper remaining on the surface of the drawing board, as shown..."

Development Of Rectangular Prism

Illustration of the development of a rectangular prism. "Assume now that the prism is laid on the drawing…

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…

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…

An illustration of Axonometric Projection, or object related by plane of projection, of a cube. The cube is drawn by having the cube resting on one side, then projecting each horizontal and vertical lines from A.

Axonometric Projection of a Cube

An illustration of Axonometric Projection, or object related by plane of projection, of a cube. The…

"The axes or edges, CG and CD, are foreshortened a like amount, while CB is foreshortened twice that of the other two. The angles of these axes being known and the reduced scale due to the foreshortening being given, the making of the projection is very simple." &mdash;Anthony, 1904

Axonometric Projection of a Rectangular Cube

"The axes or edges, CG and CD, are foreshortened a like amount, while CB is foreshortened twice that…

A rectangular cube drawn by using oblique projection. The original cube was projected parallel at a certain angle. The cube was drawn by drawing the front square in the front, then projecting it in an angle while connecting the edges.

Oblique Projection of a Rectangular Cube

A rectangular cube drawn by using oblique projection. The original cube was projected parallel at a…

The illustration of constructing a circle or ellipse using isometric drawing. The inscribed circle is transferred to the top part of the cube by creating diagonal lines through the center and series of squares.

Isometric Drawing of Circle using Square

The illustration of constructing a circle or ellipse using isometric drawing. The inscribed circle is…

A isometric drawing of the oblique and horizontal wood combined together. The image is drawn by creating the squared cube base, then, at the desired angle, draw the 3D view of the wood sticking up.

Isometric View of Oblique Timber Framed in to Horizontal Timber

A isometric drawing of the oblique and horizontal wood combined together. The image is drawn by creating…

"Suppose a hollow cube to be filled with some fluid (water or steam) at a given pressure, and to have an opening in one side that can readily be closed. The arrangement is such that when the outlet is opened, the internal pressure will remain the same. If the outlet is opened, the fluid will rush out, and if the jet is supposed to strike against a board free to move, the jet will exert a force upon the board tending to swing it in the direction of the jet." &mdash;Derr, 1911

Apparatus for Measuring Jet Stream of Steam

"Suppose a hollow cube to be filled with some fluid (water or steam) at a given pressure, and to have…

A cube-shaped building that is considered the most sacred site in Islam.

The Kaaba at Mecca

A cube-shaped building that is considered the most sacred site in Islam.

A combination of the cube (h), the octahedron (o), and the dodecahedron (d).

Galena

A combination of the cube (h), the octahedron (o), and the dodecahedron (d).

This form shows the cube (h), the dodecahedron (d), the tetrahexahedron (f), and the icositetrahedron (l).

Amalgam

This form shows the cube (h), the dodecahedron (d), the tetrahexahedron (f), and the icositetrahedron…

This form is a cube with its edges unsymmetrically truncated by the faces of the pentagonal dodecahedron.

Unsymmetrically Truncated Cube

This form is a cube with its edges unsymmetrically truncated by the faces of the pentagonal dodecahedron.

This form shows a cube modified by the tetrahedron.

Modified Cube

This form shows a cube modified by the tetrahedron.