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"A pyramid is a solid whose base is a polygon, and whose sides are triangles uniting at a common point, called the vertex." —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." — 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" — 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."—Blake, 1825

Ancient Pyramid

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

A sample exercise problem to complete the top part and create a stretched out image of the oblique hexagonal pyramid. The stretched out image is created by drawing an arc with the perimeter of the base stepped off to create an intersection point.

Development Exercise of Oblique Hexagonal Pyramid

A sample exercise problem to complete the top part and create a stretched out image of the oblique hexagonal…

The problem exercise in completing the top view and creating the development, or rolled out, image of the pentagonal pyramid.

Development Exercise of Pentagonal Pyramid

The problem exercise in completing the top view and creating the development, or rolled out, image of…

"The dihexagonal pyramid is a form of twenty-four isoceles triangular faces, each of which intersects all three of the horizontal axes differently and intersects also the vertical axis." — Ford, 1912

Dihexagonal pyramid

"The dihexagonal pyramid is a form of twenty-four isoceles triangular faces, each of which intersects…

"The ditetragonal pyramid is a form composed of sixteen isoceles trianglular faces, each of which intersects all three of the crystallographic axes, cutting the two horizontal axes at different lengths." — Ford, 1912

Ditetragonal pyramid

"The ditetragonal pyramid is a form composed of sixteen isoceles trianglular faces, each of which intersects…

Illustration showing a ditetragonal pyramid.

Ditetragonal Pyramid

Illustration showing a ditetragonal pyramid.

"The pyramid of the first order is a form consisting of eight isoceles triangular faces, each of which interesects all three crystallographic axes, the intercepts upon the two horizontal axes being equal." — Ford, 1912

First order pyramid

"The pyramid of the first order is a form consisting of eight isoceles triangular faces, each of which…

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

Frustum Pyramid

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

The volume of the frustum of any pyramid is equal to the sum of the volumes 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 bases of the frustum.

Frustum Pyramid for Volume

The volume of the frustum of any pyramid is equal to the sum of the volumes of three pyramids whose…

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part is called a frustum of a pyramid or a cone.

Pyramid Frustum

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part…

Illustration of a regular pyramid with a pentagon for a base.

Frustum of a Regular Pyramid With Pentagonal Base

Illustration of a regular pyramid with a pentagon for a base.

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

Frustum of Pentagonal Pyramid

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

"Gopura, or gate pyramid to a Hindu temple." —D'Anvers, 1895

Gate pyramid

"Gopura, or gate pyramid to a Hindu temple." —D'Anvers, 1895

Illustration of a right hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces are isosceles triangles.

Hexagonal Pyramid

Illustration of a right hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces…

Illustration of a right hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces are isosceles triangles.

Hexagonal Pyramid

Illustration of a right hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces…

Illustration of a hollow right hexagonal pyramid. The base is a hexagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Hexagonal Pyramid

Illustration of a hollow right hexagonal pyramid. The base is a hexagon and the faces are isosceles…

Illustration of a hollow right nonagonal pyramid. The base is a nonagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Nonagonal Pyramid

Illustration of a hollow right nonagonal pyramid. The base is a nonagon and the faces are isosceles…

Illustration of a hollow right octagonal pyramid. The base is an octagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Octagonal Pyramid

Illustration of a hollow right octagonal pyramid. The base is an octagon and the faces are isosceles…

Illustration of a hollow right rectangular pyramid. The base is a rectangle and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Rectangular Pyramid

Illustration of a hollow right rectangular pyramid. The base is a rectangle and the faces are isosceles…

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top.

Inverted Septagonal/Heptagonal Pyramid

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces…

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces are isosceles triangles. The pyramid is inverted, meaning that the vertex is at the bottom and the base is on top. The hidden edges are shown in this drawing.

Inverted Septagonal/Heptagonal Pyramid

Illustration of a hollow right heptagonal (septagonal) pyramid. The base is a heptagon and the faces…

Illustration of a right nonagonal pyramid with hidden edges shown. The base is a nonagon and the faces are isosceles triangles.

Nonagonal Pyramid

Illustration of a right nonagonal pyramid with hidden edges shown. The base is a nonagon and the faces…

Illustration of a right octagonal pyramid with hidden edges shown. The base is an octagon and the faces are isosceles triangles.

Octagonal Pyramid

Illustration of a right octagonal pyramid with hidden edges shown. The base is an octagon and the faces…

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the…

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid with hidden edges shown. The base is an pentagon and the…

Illustration of a right pentagonal pyramid viewed from below with hidden edges shown. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid viewed from below with hidden edges shown. The base is an…

Illustration of a right pentagonal pyramid viewed from below. The base is an pentagon and the faces are isosceles triangles.

Pentagonal Pyramid

Illustration of a right pentagonal pyramid viewed from below. The base is an pentagon and the faces…

Illustration of pentagonal pyramid used to show that the volume is equal to one third of the product of its base by its altitude.

Pentagonal Pyramid For Volume

Illustration of pentagonal pyramid used to show that the volume is equal to one third of the product…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles. The height of the pyramid is much larger then the length and width of the base.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Rectangular Pyramid

Illustration of a right rectangular pyramid with hidden edges shown. The base is a rectangle and the…

Illustration of a regular pyramid with a pentagon for a base.

Regular Pyramid With Pentagonal Base

Illustration of a regular pyramid with a pentagon for a base.

Illustration of a regular pyramid with a square for a base.

Regular Pyramid With Square Base

Illustration of a regular pyramid with a square for a base.

"The pyramid of the second order is a form composed of eight isoceles triangular faces, each of which intersects one horizontal axis and the vertical axis and is parallel to the second horizontal axis." — Ford, 1912

Second order pyramid

"The pyramid of the second order is a form composed of eight isoceles triangular faces, each of which…

Illustration of a right septagonal/heptagonal pyramid with hidden edges shown. The base is a heptagon and the faces are isosceles triangles.

Septagonal/Heptagonal Pyramid

Illustration of a right septagonal/heptagonal pyramid with hidden edges shown. The base is a heptagon…

Illustration of a non-right, or skewed, hexagonal pyramid with hidden edges shown. The base is a hexagon and the faces are isosceles triangles.

Skewed Hexagonal Pyramid

Illustration of a non-right, or skewed, hexagonal pyramid with hidden edges shown. The base is a hexagon…

Illustration of a non-right, or skewed, rectangular pyramid with hidden edges shown. The base is a rectangle and the faces are isosceles triangles.

Skewed Rectangular Pyramid

Illustration of a non-right, or skewed, rectangular pyramid with hidden edges shown. The base is a rectangle…

Illustration of triangular pyramid used to show that the volume is the limit of the sum of the volumes of a series of inscribed, or circumscribed prisms of equal altitude, if the number of prisms is indefinitely increased.

Triangular Pyramid For Volume

Illustration of triangular pyramid used to show that the volume is the limit of the sum of the volumes…

Illustration of triangular pyramid used to show that the volume is equal to one third of the product of its base by its altitude.

Triangular Pyramid For Volume

Illustration of triangular pyramid used to show that the volume is equal to one third of the product…

"Pyramidal Training." — Encyclopedia Britannica, 1893

Pyramidal Training

"Pyramidal Training." — Encyclopedia Britannica, 1893

Illustration of 2 pyramids.

Pyramids

Illustration of 2 pyramids.

An illustration of two pyramids. A pyramid is a building where the upper surfaces are triangular and converge on one point. The base of pyramids are usually quadrilateral or trilateral (but generally may be of any polygon shape), meaning that a pyramid usually has three or four sides. A pyramid's design, with the majority of the weight closer to the ground, means that less material higher up on the pyramid will be pushing down from above.

Pyramids

An illustration of two pyramids. A pyramid is a building where the upper surfaces are triangular and…

A scene from ancient Egypt, with the pyramids in the background.

Pyramids Scene

A scene from ancient Egypt, with the pyramids in the background.

Illustration of 2 right pentagonal pyramids with hidden edges shown. The pentagonal bases are congruent, but the height of the smaller pyramid is one half that of the larger.

2 Right Pentagonal Pyramids

Illustration of 2 right pentagonal pyramids with hidden edges shown. The pentagonal bases are congruent,…

Illustration of 2 right rectangular pyramids with hidden edges shown. The rectangular bases are congruent, but the height of the smaller pyramid is one half that of the larger.

2 Right Rectangular Pyramids

Illustration of 2 right rectangular pyramids with hidden edges shown. The rectangular bases are congruent,…

Egyptians using pulleys to build a pyramid.

Building the Pyramids

Egyptians using pulleys to build a pyramid.

Two triangular pyramids having equivalent bases and equal altitudes are equivalent.

Equivalent Triangular Pyramids

Two triangular pyramids having equivalent bases and equal altitudes are equivalent.

Illustration of pentagonal and triangular pyramids cut by a plane parallel to the bases.

Pyramids With Pentagonal and Triangular Bases

Illustration of pentagonal and triangular pyramids cut by a plane parallel to the bases.

Illustration of 2 regular pyramids.

Regular Pyramids

Illustration of 2 regular pyramids.

Illustration of 2 similar right pentagonal pyramids with hidden edges shown. The height of the pyramid and length of the side of the pentagon (base) on the smaller pentagonal pyramid are one half that of the larger.

Similar Pentagonal Pyramids

Illustration of 2 similar right pentagonal pyramids with hidden edges shown. The height of the pyramid…

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…

"Terminated usually by a combination of a positive and negative rhombohedron, which often are so equally developed as to give the effect of a hexagonal pyramid." — Ford, 1912

Quartz

"Terminated usually by a combination of a positive and negative rhombohedron, which often are so equally…

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

Rectangular Pyramid Cut By Plane

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

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The top section has been removed and placed next to the lower section. The lower part is known as the frustum.

Rectangular Pyramid Cut By Plane

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

Illustration of a right rectangular pyramid that has been cut by a plane parallel to the base. The top section has been removed and placed next to the lower section. The lower part is known as the frustum.

Rectangular Pyramid Cut By Plane

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