A beryl crystal, an example of a basal pinacoid.

Beryl crystal

A beryl crystal, an example of a basal pinacoid.

"The forms present upon it are two pyramids of different slope but each intersecting all three of the crystal axes when properly extended. The lower pyramid intersects the two horizontal axes at distances which are proportional to their unit lengths and if it was extended as shown by the dotted lines would also cut the vertical axis at a distance proportional to its unit length." — Ford, 1912

Sulphur crystal

"The forms present upon it are two pyramids of different slope but each intersecting all three of the…

Forms of crystals.

Crystals, Forms of

Forms of crystals.

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

"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…

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

Cube, dodecahedron and tetrahedron

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

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…

"A penetration twin, since the two individuals interpenetrate each other." &mdash; Ford, 1912

Twinned cubes

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

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a cup.

Cup

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a cup.

Cup

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a cup.

Cup

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a cup.

Cup

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

The illustration of an irregular curves for solid. The isometric projection of the curve can be drawn by the series of perpendicular lines parallel to the axis.

Drawing Irregular Isometric Curves of Solid

The illustration of an irregular curves for solid. The isometric projection of the curve can be drawn…

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the cone and parallel to the cylinder; or by cutting circles from the right cone perpendicular to the axes.

Intersection of Cylinder and Cone

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the…

An illustration showing how to construct a cycloid. "The circumference C=3.14D. Divide the rolling circle and base line C into a number of equal parts, draw through the division point the ordinates and abscissas, make aa' = 1d, bb' = 2'e, cc = 3f, then ab' and c' are points in the cycloid. In the Epicycloid and Hypocycloid the abscissas are circles and the ordinates are radii to one common center."

Construction Of A Cycloid

An illustration showing how to construct a cycloid. "The circumference C=3.14D. Divide the rolling circle…

A cylinder is a body of uniform diameter throughout its entire length, whose ends are equal parallel circles.

Cylinder

A cylinder is a body of uniform diameter throughout its entire length, whose ends are equal parallel…

A body of roller-like form, of which the longitudinal section is oblong, and the cross-section is circular.

Cylinder

A body of roller-like form, of which the longitudinal section is oblong, and the cross-section is circular.

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the cone and parallel to the cylinder; or by cutting circles from the right cone perpendicular to the axes.

Intersection of Cylinder and Cone

An illustration of finding an intersection of a cone and cylinder by either cutting the vertex of the…

Types of cylinders: vertical, horizontal, receding, and oblique.

Cylinders

Types of cylinders: vertical, horizontal, receding, and oblique.

An illustration showing how to construct a cyma, or two circle arcs that will tangent themselves, and two parallel lines at given points A and B. "Join A and B; divide AB into four equal parts and erect perpendiculars. Draw Am at right angles from A, and Bn at right angles from B; then m and n are the centers of the circle arcs of the required cyma."

Construction Of A Cyma

An illustration showing how to construct a cyma, or two circle arcs that will tangent themselves, and…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a dancer.

Dancer

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a dancer.

Dancer

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a dancer.

Dancer

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a dancer.

Dancer

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

"Monoclinic. Habit varied. Crystals usually nearly equidimensional in the three axial directions and often complex in development." &mdash; Ford, 1912

Datolite

"Monoclinic. Habit varied. Crystals usually nearly equidimensional in the three axial directions and…

"A four-sided figure, formed of 2 unequal isosceles triangles on different sides of a common base." &mdash; Williams, 1889

Deltoid

"A four-sided figure, formed of 2 unequal isosceles triangles on different sides of a common base."…

A development, or rolled out, cone where the point A is the meeting point for the sides. The development is drawn by drawing the arc by using a compass.

Development of Cone

A development, or rolled out, cone where the point A is the meeting point for the sides. The development…

A rolled out, or development, of the cylinder. The development is created by drawing the top curve with the dashed line where the folds are.

Development of Cylinder

A rolled out, or development, of the cylinder. The development is created by drawing the top curve with…

The development, or unfolded prism, of the rectangular pyramid. The sides of the prism is joined at point E for reference, and the shape of the sides are by using the reference point.

Development of Rectangle Pyramid

The development, or unfolded prism, of the rectangular pyramid. The sides of the prism is joined at…

A development, or rolled out, triangle pyramid. The image is created by making an arc at the bottom of each triangles to guide the straight lines. The triangle ABC is the base of the pyramid. When folded, the pyramid will form from the image.

Development of Triangle Pyramid

A development, or rolled out, triangle pyramid. The image is created by making an arc at the bottom…

A development, or rolled out image, of two cylinders intersecting each other. The large rectangular diagram is the main cylindrical body with a circle inside it for the other cylinder. The smaller development is the intersected cylinder. This is commonly used to illustrate pipes.

Development of Two Intersecting Cylinder

A development, or rolled out image, of two cylinders intersecting each other. The large rectangular…

Illustration of a parallelogram with diagonals AC and BD intersecting at point O.

Parallelogram With Diagonals

Illustration of a parallelogram with diagonals AC and BD intersecting at point O.

"Curved faces of the hexoctahedron are frequently observed." &mdash; Ford, 1912

Diamond

"Curved faces of the hexoctahedron are frequently observed." — Ford, 1912

Diamond.

Diamond

Diamond.

"The diploid is a rare form found only in this class. It is composed of twenty-four faces which correspond to one-half the faces of a hexoctahedron." &mdash; Ford, 1912

Diploid

"The diploid is a rare form found only in this class. It is composed of twenty-four faces which correspond…

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

Diploid and cube

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

Finding the perpendicular distance of points whose equation is x cosa + y sina = p.

Perpendicular Distance

Finding the perpendicular distance of points whose equation is x cosa + y sina = p.

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a diver.

Diver

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a diver.

Diver

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a diver.

Diver

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a diver.

Diver

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Dodecahedron.

Dodecahedron

Dodecahedron.

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

Dodecahedron and hexoctahedron

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

A dodecahedron and octahedron

Dodecahedron and octahedron

A dodecahedron and octahedron

A dodecahedron and trapezohedron.

Dodecahedron and trapezohedron

A dodecahedron and trapezohedron.

A dodecahedron and trapezohedron

Dodecahedron and trapezohedron

A dodecahedron and trapezohedron

"The faces of the deltoid dodecahedron correspond to one-half those of the trisoctahedron." &mdash; Ford, 1912

Deltoid dodecahedron

"The faces of the deltoid dodecahedron correspond to one-half those of the trisoctahedron." —…

A distorted dodecahedron

Distorted dodecahedron

A distorted dodecahedron

"A combination of of dodecahedron, trapezohedron, and hexoctahedron." &mdash; Ford, 1912

Dodecahedron, trapezohedron and hexoctahedron

"A combination of of dodecahedron, trapezohedron, and hexoctahedron." — Ford, 1912