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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 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 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 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 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 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 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 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 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 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 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 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 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 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…

"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

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.

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…

Pair of thrown dice showing two ones.

Dice Pair, 1-1

Pair of thrown dice showing two ones.

Pair of thrown dice showing a one and a two.

Dice Pair, 1-2

Pair of thrown dice showing a one and a two.

Pair of thrown dice showing two twos.

Dice Pair, 2-2

Pair of thrown dice showing two twos.

Pair of thrown dice showing a one and a three.

Dice Pair, 3-1

Pair of thrown dice showing a one and a three.

Pair of thrown dice showing a two and a three.

Dice Pair, 3-2

Pair of thrown dice showing a two and a three.

Pair of thrown dice showing two threes.

Dice Pair, 3-3

Pair of thrown dice showing two threes.

Pair of thrown dice showing a four and a one.

Dice Pair, 4-1

Pair of thrown dice showing a four and a one.

Pair of thrown dice showing a four and a two.

Dice Pair, 4-2

Pair of thrown dice showing a four and a two.

Pair of thrown dice showing a four and a three.

Dice Pair, 4-3

Pair of thrown dice showing a four and a three.

Pair of thrown dice showing two fours.

Dice Pair, 4-4

Pair of thrown dice showing two fours.

Pair of thrown dice showing a five and a one.

Dice Pair, 5-1

Pair of thrown dice showing a five and a one.

Pair of thrown dice showing a five and a two.

Dice Pair, 5-2

Pair of thrown dice showing a five and a two.

Pair of thrown dice showing a five and a three.

Dice Pair, 5-3

Pair of thrown dice showing a five and a three.

Pair of thrown dice showing a five and a four.

Dice Pair, 5-4

Pair of thrown dice showing a five and a four.

Pair of thrown dice showing a pair of fives.

Dice Pair, 5-5

Pair of thrown dice showing a pair of fives.

Pair of thrown dice showing a six and a one.

Dice Pair, 6-1

Pair of thrown dice showing a six and a one.

Pair of thrown dice showing a six and a two.

Dice Pair, 6-2

Pair of thrown dice showing a six and a two.

Pair of thrown dice showing a six and a three.

Dice Pair, 6-3

Pair of thrown dice showing a six and a three.

Pair of thrown dice showing a six and a four.

Dice Pair, 6-4

Pair of thrown dice showing a six and a four.

Pair of thrown dice showing a six and a five.

Dice Pair, 6-5

Pair of thrown dice showing a six and a five.

Pair of thrown dice showing a pair of sixes.

Dice Pair, 6-6

Pair of thrown dice showing a pair of sixes.

A die with face of five.

Die Showing Five

A die with face of five.

A die with face of four.

Die Showing Four

A die with face of four.

A die with face of one.

Die Showing One

A die with face of one.

A die with face of six.

Die Showing Six

A die with face of six.

A die with face of three.

Die Showing Three

A die with face of three.

A die with face of two.

Die Showing Two

A die with face of two.

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

Diploid and cube

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

A flashcard featuring an illustration of a Cube

Flashcard of a Cube

A flashcard featuring an illustration of a Cube

This image shows one of Friedrich Froebel's divided cube (this one divided into many smaller cubes and prisms). Froebel's cubes were used to encourage creativity in kindergarten-age children. The children could rearrange the smaller shapes into combinations that showed life, knowledge, and beauty.

Froebel's Divided Cube (Complex)

This image shows one of Friedrich Froebel's divided cube (this one divided into many smaller cubes and…

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).

Development of an isometric of a cube.

Development of an Isometric of a Cube

Development of an isometric of a cube.

This form shows a cube modified by the tetrahedron.

Modified Cube

This form shows a cube modified by the tetrahedron.

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…

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.

"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…

Three large rhombuses for pattern block set.

Large Rhombuses for Pattern Block Set

Three large rhombuses for pattern block set.

"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…