ClipArt of pyramids with various bases. A pyramid is a solid geometric figure with a base that is a polygon and sides that are triangular in shape and meet at a common point at the top, known as the apex.

Illustration showing that the volume of 2 triangular pyramids, having the same trihedral angle of the one equal to a trihedral angle of the other, are to each other as the products of the three edges of these trihedral angles.

Triangular Pyramids for Volume

Illustration showing that the volume of 2 triangular pyramids, having the same trihedral angle of the…

The illustration of a rectangular pyramid unfolded by creating edges equal length to the base and meeting at point E.

Development of Rectangular Pyramid

The illustration of a rectangular pyramid unfolded by creating edges equal length to the base and meeting…

"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

Regular Tetrahedron

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

"This is a form composed of twelve isoceles triangular faces, each of which intersects two of the horizontal axes equally, the third and immediate horizontal axis at one-half this distance, and also intersects the vertical axis." — Ford, 1912

Pyramid of the second order

"This is a form composed of twelve isoceles triangular faces, each of which intersects two of the horizontal…

"It consists of four isoceles triangular faces which intersect all three of the crystallographic axes, the intercepts on the two horizontal axes being equal. The faces correspond in their position to the alternating faces of the tetragonal pyramid of the first order." — Ford, 1912

Sphenoid

"It consists of four isoceles triangular faces which intersect all three of the crystallographic axes,…

"It consists of four isoceles triangular faces which intersect all three of the crystallographic axes, the intercepts on the two horizontal axes being equal. The faces correspond in their position to the alternating faces of the tetragonal pyramid of the first order." — Ford, 1912

Sphenoid

"It consists of four isoceles triangular faces which intersect all three of the crystallographic axes,…

"It consists of four isoceles triangular faces which intersect all three of the crystallographic axes, the intercepts on the two horizontal axes being equal. The faces correspond in their position to the alternating faces of the tetragonal pyramid of the first order. There maybe different sphenoids, depending upon their varying intersections with the vertical axes. There may also be a positive and a negative sphenoid, the combination of the two being represented." — Ford, 1912

Sphenoid, positive and negative

"It consists of four isoceles triangular faces which intersect all three of the crystallographic axes,…

Illustration of the intersection of a square pyramid and a plane.

Intersection of Square Pyramid and a Plane

Illustration of the intersection of a square pyramid and a plane.

Illustration of the intersection of a square pyramid and a plane.

Intersection of Square Pyramid and a Plane

Illustration of the intersection of a square pyramid and a plane.

"This is bounded by four equilateral triangles and is identical with the regular tetrahedron of geometry." -The Encyclopedia Britannica 1910

Tetrahedron

"This is bounded by four equilateral triangles and is identical with the regular tetrahedron of geometry."…

"The tetrahedron is a form composed of four equilateral triangular faces, each of which intersects all of the crystallographic axes at equal lengths. It can be considered as derived from the octahedron of the Normal Class by the omission of the alternate faces and the extension of the others. If the other four faces of the octahedron had been extended, the tetrahedron resulting would have had a different orientation, known as the negative tetrahedron." — Ford, 1912

Negative tetrahedron

"The tetrahedron is a form composed of four equilateral triangular faces, each of which intersects all…

"The tetrahedron is a form composed of four equilateral triangular faces, each of which intersects all of the crystallographic axes at equal lengths. It can be considered as derived from the octahedron of the Normal Class by the omission of the alternate faces and the extension of the others." — Ford, 1912

Positive tetrahedron

"The tetrahedron is a form composed of four equilateral triangular faces, each of which intersects all…

"If a positive and negative tetrahedron occured together with equal development, the resulting crystal could not be distinguished from an octahedron, unless, as is usually the case, the faces of the two forms showed different lusters, etchings, or striations that would serve to differentiate them." — Ford, 1912

Positive and negative tetrahedrons

"If a positive and negative tetrahedron occured together with equal development, the resulting crystal…

Development of a triangular pyramid.

Development of a Triangular Pyramid

Development of a triangular pyramid.

Plan and elevation of a triangular pyramid.

Plan and Elevation of a Triangular Pyramid

Plan and elevation of a triangular pyramid.

Illustration of the intersection of a triangular pyramid and a plane.

Intersection of Triangular Pyramid and a Plane

Illustration of the intersection of a triangular pyramid and a plane.