An illustration of a hen, cat, dog and horse standing on top of one another to see into a window.

Animals Looking Through Window

An illustration of a hen, cat, dog and horse standing on top of one another to see into a window.

"A complex crystal of apatite with the faces of a third-order pyramid upon it." — Ford, 1912

Apatite

"A complex crystal of apatite with the faces of a third-order pyramid upon it." — Ford, 1912

"Hexagonal; tri-pyramidal. Crystals usually long prismatic in habit; sometimes short prismatic or tabular. Usually terminated by prominent pyramid of first order and frequently a basal plane." — Ford, 1912

Apatite

"Hexagonal; tri-pyramidal. Crystals usually long prismatic in habit; sometimes short prismatic or tabular.…

"Tetragonal. Usually shows a combination of prism of second order, pyramid of first and basal plane." — Ford, 1912

Apophyllite

"Tetragonal. Usually shows a combination of prism of second order, pyramid of first and basal plane."…

"Orthorhombic. Acicular pyramidal; consisting of a prism terminated by a combination of a very steep pyramid and brachydome." — Ford, 1912

Aragonite

"Orthorhombic. Acicular pyramidal; consisting of a prism terminated by a combination of a very steep…

An image of a bald cypress, in pyramidal cultivated form. It is otherwise known as taxodium distichum, and is native to the southeastern United States.

Bald Cypress in Cultivated Form

An image of a bald cypress, in pyramidal cultivated form. It is otherwise known as taxodium distichum,…

Illustration of a conical bifrustum created by three parallel planes of circles with the middle plane largest. The top and bottom circles are congruent. It is constructed from two congruent frustums across a plane of symmetry.

Conical Bifrustum

Illustration of a conical bifrustum created by three parallel planes of circles with the middle plane…

Illustration of a decagonal bifrustum created by three parallel planes of decagons with the middle plane largest. The top and bottom decagons are congruent. It can be constructed from two congruent frustums across a plane of symmetry, or as a bipyramid with truncated vertices.

Decagonal Bifrustum

Illustration of a decagonal bifrustum created by three parallel planes of decagons with the middle plane…

Illustration of a hexagonal bifrustum created by three parallel planes of hexagons with the middle plane largest. The top and bottom hexagons are congruent. It can be constructed from two congruent frustums across a plane of symmetry, or as a bipyramid with truncated vertices.

Hexagonal Bifrustum

Illustration of a hexagonal bifrustum created by three parallel planes of hexagons with the middle plane…

Illustration of a octagonal bifrustum created by three parallel planes of octagons with the middle plane largest. The top and bottom octagons are congruent. It can be constructed from two congruent frustums across a plane of symmetry, or as a bipyramid with truncated vertices.

Octagonal Bifrustum

Illustration of a octagonal bifrustum created by three parallel planes of octagons with the middle plane…

Illustration of a square bifrustum created by three parallel planes of squares with the middle plane largest. The top and bottom squares are congruent. It can be the combination of two congruent frustums across a plane of symmetry, or as a bipyramid with truncated vertices.

Square Bifrustum

Illustration of a square bifrustum created by three parallel planes of squares with the middle plane…

Brawl among Egyptian boatmen. Carving from the tomb of Ptah-hetep during the Pyramid age.

Egyptian Boatmen Fighting

Brawl among Egyptian boatmen. Carving from the tomb of Ptah-hetep during the Pyramid age.

"Tetragonal. Common forms are prisms and pyramids of first and second orders." — Ford, 1912

Cassiterite

"Tetragonal. Common forms are prisms and pyramids of first and second orders." — Ford, 1912

Illustration of a pyramid circumscribed about a cone.

Pyramid Circumscribed About a Cone

Illustration of a pyramid circumscribed about a cone.

Illustration of a pyramid inscribed in a cone.

Pyramid Inscribed in a Cone

Illustration of a pyramid inscribed in a cone.

"Hexagonal-rhombohedral. Crystals usually prismatic in habit or tapering hexagonal pyramids." — Ford, 1912

Corundum

"Hexagonal-rhombohedral. Crystals usually prismatic in habit or tapering hexagonal pyramids." —…

"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…

An illustration of a cube divided into 6 equal pyramids to illustrate how volume can be found.

Cube for Illustrating Volume

An illustration of a cube divided into 6 equal pyramids to illustrate how volume can be found.

"Cyrus caught sight of his brother Artaxerxes, whose person was revealed by the flight of his troops, when, maddened at once by rage and ambition, he shouted out, "I see the man!" and rushed at him with his handful of companions. Hurling his javelin at his brother, he wounded him in the breast, but was himself speedily overbourne by superior numbers and slain on the spot." — Smith, 1882

Tomb of Cyrus

"Cyrus caught sight of his brother Artaxerxes, whose person was revealed by the flight of his troops,…

The length of the Dashur pyramid is approximately 200 feet.

Pyramid of Dashur

The length of the Dashur pyramid is approximately 200 feet.

Illustration showing a tetragonal deuteropyramid.

Tetragonal Deuteropyramid

Illustration showing a tetragonal deuteropyramid.

"This form consists of twelve isoceles triangular faces, each of which intersects two of the horizontal crystallographic axes equally, is parallel to the third horizontal axis and intersects the vertical axis." — Ford, 1912

Pyramid of the first order

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

A flashcard featuring an illustration of a Pyramid with a Hexagonal Base

Flashcard of a Pyramid with a Hexagonal Base

A flashcard featuring an illustration of a Pyramid with a Hexagonal Base

A flashcard featuring an illustration of a Pyramid with a Pentagonal Base

Flashcard of a Pyramid with a Pentagonal Base

A flashcard featuring an illustration of a Pyramid with a Pentagonal Base

A flashcard featuring an illustration of a Pyramid with a Rectangular Base

Flashcard of a Pyramid with a Rectangular Base

A flashcard featuring an illustration of a Pyramid with a Rectangular Base

A flashcard featuring an illustration of a Pyramid with a Square Base

Flashcard of a Pyramid with a Square Base

A flashcard featuring an illustration of a Pyramid with a Square Base

A flashcard featuring an illustration of a Pyramid with a Triangular Base

Flashcard of a Pyramid with a Triangular Base

A flashcard featuring an illustration of a Pyramid with a Triangular Base

Diagram used to prove the theorem: "The volume of the frustum of a pyramid (cone) is equal to the sum of three pyramids (cones) whose common altitude is the altitude of the frustum and whose bases are respectively the upper base, the lower base, and a mean proportional between them."

Volume of Frustum of a Pyramid

Diagram used to prove the theorem: "The volume of the frustum of a pyramid (cone) is equal to the sum…

Projection of a frustum of a square pyramid.

Projection of Frustum of Square Pyramid

Projection of a frustum of a square pyramid.

The frustum of a pyramid is the portion of a pyramid included between the base and a section parallel to the base.

Pyramid Frustum

The frustum of a pyramid is the portion of a pyramid included between the base and a section parallel…

The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and the mean proportional between the two bases of the frustum.

Triangular Pyramid Frustum

The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude…

Two pyramids and a sphinx near Gizeh, Egypt, built during the 25th century. These three structures rank high in superiority to other pyramids due to their size and magnificence.

Pyramids of Gizeh

Two pyramids and a sphinx near Gizeh, Egypt, built during the 25th century. These three structures rank…

A hand holding a square pyramid, suspended by a string.

Hand and pyramid

A hand holding a square pyramid, suspended by a string.

Illustration of a right hexagonal pyramid that has been cut by a plane parallel to the base. The lower part is known as the frustum.

Hexagonal Pyramid Cut By Plane

Illustration of a right hexagonal pyramid that has been cut by a plane parallel to the base. The lower…

An image of a hexagonal pyramid stretched out. The length of the edges are equal plane, and intersects the at the perimeter of the base.

Development of Hexagonal Pyramid

An image of a hexagonal pyramid stretched out. The length of the edges are equal plane, and intersects…

Cleopatra's name, written in hieroglyphics.

Hieroglyphics, Cartouche of Cleopatra

Cleopatra's name, written in hieroglyphics.

Genus Juniperus of the cypress family Cupressaceae. This juniper is in pyramidal form, found in Potomac Valley, Washington, D.C.

Juniper in Pyramidal Form

Genus Juniperus of the cypress family Cupressaceae. This juniper is in pyramidal form, found in Potomac…

"<em>A</em>, pyramids of the kidney; <em>B</em>, apices, or papillae, of the pyramids; <em>C</em>, pelvis of the kidney; <em>D</em>, upper end of the ureter</em>." &mdash; Blaisedell, 1904

Kidney

"A, pyramids of the kidney; B, apices, or papillae, of the pyramids; C, pelvis…

"The third pyramid on the ridge of Gizeh was built by Menkera, a successor of Khafra and fourth or fifth king of Dynasty IV. This structure is but two hundred and thirty-three feet at the base, and the slant height two hundred and sixty-two feet. The Menkera pyramid stands on looser soil than its more ambitious sisters, and the substructure is consequently of greater relative proportions. Part of the exterior consists of polished slabs of granite. The sepulchral chamber within is double, one apartment being behind the other." &mdash;Ridpath, 1885

Sarcophagus of Menkera

"The third pyramid on the ridge of Gizeh was built by Menkera, a successor of Khafra and fourth or fifth…

"Prisims with edges parallel to neither of the axes OX and OY...are usually called hemi-pyramids." -The Encyclopedia Britannica

Monoclinic Axes and Hemi-pyramid

"Prisims with edges parallel to neither of the axes OX and OY...are usually called hemi-pyramids." -The…

Illustration of a right octagonal pyramid, with hidden edges shown, that has been cut by a plane parallel to the base. The lower part is known as the frustum.

Octagonal Pyramid Cut By Plane

Illustration of a right octagonal pyramid, with hidden edges shown, that has been cut by a plane parallel…

Illustration of a right octagonal pyramid that has been cut by a plane parallel to the base. The lower part is known as the frustum.

Octagonal Pyramid Cut By Plane

Illustration of a right octagonal pyramid that has been cut by a plane parallel to the base. The lower…

Illustration of a hollow octagonal pyramid that has been cut by a plane parallel to the base. The top section has been removed and the remaining section has been turned upside down. It is known as the frustum of the pyramid.

Frustum Of A Octagonal Pyramid

Illustration of a hollow octagonal pyramid that has been cut by a plane parallel to the base. The top…

Diagram used to prove the theorem: "If a pyramid is cut by a plane parallel to the base, the edges are divided proportionally, and the section is a polygon similar to the base."

Pyramid Cut By Plane

Diagram used to prove the theorem: "If a pyramid is cut by a plane parallel to the base, the edges are…

Orthogonal projection of a closed plane-faced polyhedron.

Polyhedron

Orthogonal projection of a closed plane-faced polyhedron.

Orthogonal projection of a closed plane-faced polyhedron.

Polyhedron

Orthogonal projection of a closed plane-faced polyhedron.

A volume of a truncated right triangular prism is equal to the product of its base by one third the sum of its lateral edges.

Truncated Right Triangular Prism for Volume

A volume of a truncated right triangular prism is equal to the product of its base by one third the…

A volume of a truncated right triangular prism is equal to the product of its base by one third the sum of its lateral edges.

Truncated Right Triangular Prism for Volume

A volume of a truncated right triangular prism is equal to the product of its base by one third the…

Diagram showing how "A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism and whose vertices are the three vertices of the upper base."

Truncated Triangular Prism

Diagram showing how "A truncated triangular prism is equivalent to the sum of three pyramids whose common…

A truncated triangular prism is equivalent to the sum of three pyramids, whose common base is the base of the prism and whose vertices are the three vertices of the inclined section.

Truncated Triangular Prism for Volume

A truncated triangular prism is equivalent to the sum of three pyramids, whose common base is the base…

A truncated triangular prism is equivalent to the sum of three pyramids, whose common base is the base of the prism and whose vertices are the three vertices of the inclined section.

Truncated Triangular Prism for Volume

A truncated triangular prism is equivalent to the sum of three pyramids, whose common base is the base…

"An orthorhombic pyramid has eight triangular faces, each of which intersects all three of the crystallographic axes." &mdash; Ford, 1912

Pyramid

"An orthorhombic pyramid has eight triangular faces, each of which intersects all three of the crystallographic…

An architectural structure of solid masonry, built for various purposes in different parts of the world.

Pyramid

An architectural structure of solid masonry, built for various purposes in different parts of the world.

"If a pyramid be cut by a plane, parallel to the base, so as to form two parts, the lower part is called the frustum of the pyramid." &mdash; Hallock, 1905

Pyramid

"If a pyramid be cut by a plane, parallel to the base, so as to form two parts, the lower part is called…

A pyramid

Pyramid

A pyramid

"A pyramid is a solid whose base is a polygon, and whose sides are triangles uniting at a common point, called the vertex." &mdash;Hallock 1905

Pryamid

"A pyramid is a solid whose base is a polygon, and whose sides are triangles uniting at a common point,…

Illustration used to compare the volumes of a pyramid and a prism by emptying sand from the pyramid into the prism.

Comparative Volumes Of A Pyramid And Prism

Illustration used to compare the volumes of a pyramid and a prism by emptying sand from the pyramid…

"a shows a young tree with its second year's growth, the upright shoot of the maiden tree having been moderately headed back, being left longer if the buds near the base promise to break freely, or cut shorter if they are weak and wanting in vigour. The winter pruning, carried out with the view to shape the tree into a well-grown pyramid, would be effected at the places marked by a cross line." &mdash; Encyclopedia Britannica, 1893

Pyramid Pruning

"a shows a young tree with its second year's growth, the upright shoot of the maiden tree having been…

"Pyramid and Sphinx at Gizeh" &mdash; Morey, 1903

Pyramid Sphinx

"Pyramid and Sphinx at Gizeh" — Morey, 1903

"The pyramids of Egypt are well entitled to a place among the most interesting curiosities in the world. The principal ones stand opposite Cairo, on the west side of the river Nile. They are built of stones, which overleap each other, and thus form steps from the bottom to the top. The perpendicular height of the largest is about 500 feet, and the area of its basis contains nearly 500,000 square feet, or something more than eleven English acres of ground."&mdash;Blake, 1825

Ancient Pyramid

"The pyramids of Egypt are well entitled to a place among the most interesting curiosities in the world.…