A combination of a tetrahedron and a rhombic dodecahedron.

Combination of Tetrahedron and Rhombic Dodecahedron

A combination of a tetrahedron and a rhombic dodecahedron.

"...a combination of these two tetrahedra, and represents a crystal of blende, in which the four larger faces are dull and striated, whilst the four smaller are bright and smooth." -The Encyclopedia Britannica 1910

Combination of two Tetrahedra

"...a combination of these two tetrahedra, and represents a crystal of blende, in which the four larger…

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

Cube, dodecahedron and tetrahedron

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

Illustration showing the derivation of Tetrahedron from an Octahedron.

Tetrahedron From Octahedron

Illustration showing the derivation of Tetrahedron from an Octahedron.

Illustration of regular polyhedrons: tetrahedron, hexahedron, octahedron, dodecahedron, icosahedron.

Regular Polyhedrons

Illustration of regular polyhedrons: tetrahedron, hexahedron, octahedron, dodecahedron, icosahedron.

Diagram used to prove the theorem: "Two similar polyhedrons may be decomposed into the same number of tetrahedrons, similar each to each , and similarly placed."

Two Similar Polyhedrons

Diagram used to prove the theorem: "Two similar polyhedrons may be decomposed into the same number of…

"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…

Illustration containing a tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron, placed next to each other.

Various Solid Forms

Illustration containing a tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron, placed…

"Isometric; tetrahedral. Tetrahedron form." — Ford, 1912

Sphalerite

"Isometric; tetrahedral. Tetrahedron form." — Ford, 1912

Illustration of a sphere inscribed in a tetrahedron.

Sphere Inscribed in Tetrahedron

Illustration of a sphere inscribed in a tetrahedron.

Illustration of a sphere inscribed in a tetrahedron.

Sphere Inscribed in Tetrahedron

Illustration of a sphere inscribed in a tetrahedron.

"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."…

Principal forms of the isometric system: tetrahedron.

Tetrahedron

Principal forms of the isometric system: tetrahedron.

"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

Tetrahedron and cube

"A combination of cube and tetrahedron. It will be noted that the tetrahedron faces truncate the alternate…

"The combination of tetrahedron and dodecahedron." — Ford, 1912

Tetrahedron and dodecahedron

"The combination of tetrahedron and dodecahedron." — Ford, 1912

"A combination of tetrahedron and tristetrahedron." — Ford, 1912

Tetrahedron and tristetrahedron

"A combination of tetrahedron and tristetrahedron." — Ford, 1912

"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…

Pattern that can be cut out and folded to construct a regular tetrahedron. Fold on the dotted lines, and keep the edges in contact by the glued strips of paper.

Pattern for Tetrahedron

Pattern that can be cut out and folded to construct a regular tetrahedron. Fold on the dotted lines,…

"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…

Diagram used to prove the theorem: "Two tetrahedrons having a trihedral angle in each equal, are to each other as the products of the including edges."

Two Proportional Tetrahedrons

Diagram used to prove the theorem: "Two tetrahedrons having a trihedral angle in each equal, are to…