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Principal forms of the hexagonal system: hexagonal pyramid.

Hexagonal Pyramid Second Order

Principal forms of the hexagonal system: hexagonal pyramid.

Principal forms of the hexagonal system: dihexagonal pyramid.

Dihexagonal Pyramid

Principal forms of the hexagonal system: dihexagonal pyramid.

Principal forms of the triclinic system: tryclinic pyramid

Triclinic Pyramid

Principal forms of the triclinic system: tryclinic pyramid

Illustration of a frustum of a pyramid having a rectangular base and a hole passing through the center of the frustum.

Frustum Of A Rectangular Pyramid With Hole

Illustration of a frustum of a pyramid having a rectangular base and a hole passing through the center…

Illustration of the projection of a hexagonal pyramid that is in a right position.

Projection Of Hexagonal Pyramid

Illustration of the projection of a hexagonal pyramid that is in a right position.

Illustration of the projection of a hexagonal pyramid that is obliquely inclined.

Projection Of Hexagonal Pyramid

Illustration of the projection of a hexagonal pyramid that is obliquely inclined.

Illustration of the development of a pyramid. When the pyramid covered in paper (figure a) is rolled out on a flat surface, the result is shown in figure b.

Development Of Pyramid

Illustration of the development of a pyramid. When the pyramid covered in paper (figure a) is rolled…

Illustration showing the cone being treated as a many-sided pyramid.

Relation Of Pyramid To Cone

Illustration showing the cone being treated as a many-sided pyramid.

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…

Diagram used to prove the theorem: "Two triangular pyramids having equivalent bases and equal altitudes are equivalent."

Equivalent Triangular Pyramids

Diagram used to prove the theorem: "Two triangular pyramids having equivalent bases and equal altitudes…

Diagram used to prove the theorem: "The volume of a triangular pyramid is equal to one third of a triangular prism of the same base and altitude."

Volume of Triangular Pyramid

Diagram used to prove the theorem: "The volume of a triangular pyramid is equal to one third of a triangular…

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…

Illustration of an inverted pentagonal pyramid. It is pyramid with a regular pentagon for its base.

Inverted Pentagonal Pyramid

Illustration of an inverted pentagonal pyramid. It is pyramid with a regular pentagon for its base.

Illustration of the bottom part of an icosahedron. The base consists of a regular pyramid, upon which equilateral triangles are inserted to form the next section of the icosahedron.

Part of an Icosahedron

Illustration of the bottom part of an icosahedron. The base consists of a regular pyramid, upon which…

Illustration of the steps to a construction of an icosahedron. The base consists of a regular pyramid, upon which equilateral triangles are inserted to form the next section of the icosahedron, followed by another pyramid.

Partial Construction of an Icosahedron

Illustration of the steps to a construction of an icosahedron. The base consists of a regular pyramid,…

Illustration of an icosahedron.

Icosahedron

Illustration of an icosahedron.

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…

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.

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may be copied in the new position distance from the ground line to any point in the top view be unchanged, hence the new top view may be found by projecting up from the front view and across from the original top view" —French, 1911

Revolution About Axis Perpendicular to V

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may…

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may be copied in the new position distance from the ground line to any point in the top view be unchanged, hence the new top view may be found by projecting up from the front view and across from the original top view" —French, 1911

Revolution About Axis Forward or Back

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may…

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…

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…

Exercise problem to develop, or rolled out, image of the triangular pyramid by creating an equal length of the edges of each triangle.

Development Exercise of Triangular Pyramid

Exercise problem to develop, or rolled out, image of the triangular pyramid by creating an equal length…

A pentagonal pyramid problem exercise to complete the top view of the image, and development, or rolled out image, of the pyramid.

Development Exercise of Pentagonal Pyramid

A pentagonal pyramid problem exercise to complete the top view of the image, and development, or rolled…

A problem exercise creating a stretched out or developed image of the octagonal light shade by using the hexagonal pyramid development method.

Development Exercise of Octagonal Light Shade

A problem exercise creating a stretched out or developed image of the octagonal light shade by using…

A sample exercise problem in completing the top part of the hexagonal pyramid and to create a development, or stretched out, of the image by creating edges at equal lengths, and revolving the sides.

Development Exercise of Hexagonal Pyramid

A sample exercise problem in completing the top part of the hexagonal pyramid and to create a development,…

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…

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 illustration showing the projection of the triangles from the triangle pyramid as shown on top. This projection helps create the development of the pyramid by connecting each projection together.

Triangle Pyramid Side Projections

The illustration showing the projection of the triangles from the triangle pyramid as shown on top.…

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…

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…

Egyptians using pulleys to build a pyramid.

Building the Pyramids

Egyptians using pulleys to build a pyramid.

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…

"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." —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…

The length of the Dashur pyramid is approximately 200 feet.

Pyramid of Dashur

The length of the Dashur pyramid is approximately 200 feet.

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…

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,…

"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 Pharaoh of Ancient Egypt. He reigned from 2589 to 2566 BC, and is known for being the builder of the Great Pyramid of Giza.

Khufu

A Pharaoh of Ancient Egypt. He reigned from 2589 to 2566 BC, and is known for being the builder of the…

"The pyramid when completed had a height of 481 feet. It is now 451 feet high. Its base covers 13 acres. Some of the blocks of white limestone used in construction weigh 50 tons. The facing of polished stone was gradually removed for building purposes by the Arabs. On the northern side of the pyramid a narrow entrance, once carefully concealed, opens into tortuous passages which lead to the central vault. Here the sarcophagus of the king was placed. This chamber was long since entered and its contents rifled."—Webster, 1913

The Great Pyramid of Giza

"The pyramid when completed had a height of 481 feet. It is now 451 feet high. Its base covers 13 acres.…

"This colossal figure, human-headed and lion-bodied, is hewn from the natural rock. The body is about 150 feet long, the paws 50 feet, the head 30 feet. The height from the base of the top of the head is 70 feet. Except for its head and shoulders, the figure has been buried for centuries in the desert sand. The eyes, nose, and beard have been mutilated by the Arabs. The face is probably that of one of the pyramid kings."—Webster, 1913

The Great Sphinx

"This colossal figure, human-headed and lion-bodied, is hewn from the natural rock. The body is about…

A portion of detail from a photograph of the Great Pyramid in Egypt.

Detail of the Great Pyramid

A portion of detail from a photograph of the Great Pyramid in Egypt.

"Supposed portrait of one of the overseers of the work on the Great Pyramid. This is one of the masterpieces of Egyptian sculpture."—Myers, 1904

The Sheikh-El-Beled

"Supposed portrait of one of the overseers of the work on the Great Pyramid. This is one of the masterpieces…

The common name of <I>Araucaria imbricata</I> is monkey puzzle. The tree has a pyramid shaped habit of growth. The branches have upward curving tips.

Araucaria Imbricata

The common name of Araucaria imbricata is monkey puzzle. The tree has a pyramid shaped habit of growth.…

This form is bounded by forty-eight similar scalene triangles. Its solid angles are of three kinds: six octahedral, at the extremities of the principal axes; eight hexahedral, at the extremities of the trigonal axes; and twelve tetrahedral, at the extremities of the digonal axes. Naumann's symbol for this form is m 0 n; Dana's, m-n.

Hexoctahedron

This form is bounded by forty-eight similar scalene triangles. Its solid angles are of three kinds:…

This illustration shows the union of a pyramid and a prism of the same order.

Union of a Pyramid and a Prism of the Same Order

This illustration shows the union of a pyramid and a prism of the same order.

This illustration shows the union of a pyramid and a prism of different orders.

Union of a Pyramid and a Prism of Different Orders

This illustration shows the union of a pyramid and a prism of different orders.

This form shows the planes given on a crystal of hydrous nickel sulphate: the basal pinacoid, (c); three pyramids of the second order, (m), (o), and (q); two pyramids of the first order, (n) and (p); and the prisms of the first and second orders, (r) and (s).

Hydrous Nickel Sulphate

This form shows the planes given on a crystal of hydrous nickel sulphate: the basal pinacoid, (c); three…

This form shows a very complex combination of thirteen tetragonal forms occuring on the mineral Vesuvianite: the prism of the first order, (d); prism of the second order, (M); basal pinacoid, (s); three pyramids of the first order, (c), (b), and (u); the ditetragonal prism (f); and the four ditetragonal pyramids (z), (x), (e), and (a).

Vesuvianite

This form shows a very complex combination of thirteen tetragonal forms occuring on the mineral Vesuvianite:…

Also known as Stolzite, this crystal is bounded by the unit pyramid of the first order, P, {111} (o), and by the prism of the third order, (p).

Lead Tungstate

Also known as Stolzite, this crystal is bounded by the unit pyramid of the first order, P, {111} (o),…

Also known as Fergusonite, this crystal shows the basal pinacoid, (c); the unit pyramid, (s); and the pyramid and prism of the third order, (z) and (r) respectively.

Yttrium Niobate

Also known as Fergusonite, this crystal shows the basal pinacoid, (c); the unit pyramid, (s); and the…

This figure shows a combination of forms sometimes observed on the silicate Scapolite, with the unit pyramid, (o); the prisms of the first and second orders, (M) and (b) respectively; and the pyramid of the third order, (s).

Scapolite

This figure shows a combination of forms sometimes observed on the silicate Scapolite, with the unit…

This crystal of Calcium Phosphate, Apatite, represents a complex combination of hexagonal hemihedral forms produced by the pyramidal selection. The nine forms comprise the basal pinacoid ,(P); the prism of the first order, (M); second order, (u); and third order, (h); three pyramids of the first order, (r), (x), and (y); one pyramid of the second order, (s); and one of the third order, (m).

Calcium Phosphate, Apatite

This crystal of Calcium Phosphate, Apatite, represents a complex combination of hexagonal hemihedral…

This form shows the fundamental prism (p) on a crystal of topaz, in combination with another prism, (p'); the basal pinacoid, (c); the brachydome, (g); and the four pyramids, (o), (o'), (o''), and (x).

Orthorhombic Crystal of Topaz

This form shows the fundamental prism (p) on a crystal of topaz, in combination with another prism,…

In the tetragonal system, the unit pyramid of the second order is the most common twinning plane. This is represented here as it occurs on crystals of Zircon, bounded by the forms (m), (u), (p), and (o).

Zircon (Twinning)

In the tetragonal system, the unit pyramid of the second order is the most common twinning plane. This…

"Then Joseph could not refrain himself before all them that stood before him; and he cried, Cause every man to go out from me. And there stood no man with him, while Joseph made himself known unto his brethren." Genesis 45:1 ASV <p> Illustration of Joseph finally revealing himself to his brothers as they stand around him in awe. He leans over and hugs Benjamin. Six of the brothers kneel on the ground in front of Joseph. A seat or throne can be seen partially on the left. Through the two large open windows, a pyramid, camels, palm trees, buildings, and an obelisk are visible.

Joseph Reveals Himself to His Brothers and Embraces Benjamin

"Then Joseph could not refrain himself before all them that stood before him; and he cried, Cause every…

"And Joseph made ready his chariot, and went up to meet Israel his father, to Goshen; and he presented himself unto him, and fell on his neck, and wept on his neck a good while. And Israel said unto Joseph, Now let me die, since I have seen thy face, that thou art yet alive." Genesis 46:29-30 <p>Illustration of Joseph as he embraces Jacob. All of Jacob's family and people stand behind him. They are dressed as shepherds and bring sheep with them. Horses and Egyptians stand behind Joseph. Two of the Egyptians hold parasols. A pyramid can be seen in the background of the direction from which Joseph has come.

Joseph Greets His Father Jacob and His Family

"And Joseph made ready his chariot, and went up to meet Israel his father, to Goshen; and he presented…

"And Moses and Aaron went in unto Pharaoh, and they did so, as Jehovah had commanded: and Aaron cast down his rod before Pharaoh and before his servants, and it became a serpent." Exodus 7:10 ASV <p>Illustration of Moses and Aaron standing before Pharaoh and his advisers. Aaron holds the tale of a serpent that used to be his rod. Moses stands next to him and gestures toward the serpent. Pharaoh, wearing a crown, holding a sceptre, and sitting on a throne, stares at the snake. His arm is outstretched. One of Pharaoh's servants gapes at the scene. Others stand behind him, befuddled. A doorway displays a pyramid and palm trees in the background.

Aaron's Rod Turning into a Serpent Before Pharaoh and His Magicians

"And Moses and Aaron went in unto Pharaoh, and they did so, as Jehovah had commanded: and Aaron cast…

"And the blood shall be to you for a token upon the houses where ye are: and when I see the blood, I will pass over you, and there shall no plague be upon you to destroy you, when I smite the land of Egypt." Exodus 12:13 ASV <p>Illustration of the angel of death passing by the door of an Israelite home. The door is marked on the top side with the smeared blood of an unblemished lamb. The angel hovers over the ground and carries a sword in his right hand. Inside the house, a family can be seen gathered around the table with the slaughtered lamb on it. They are observing the first Passover. Behind the angel, a child lies dead in the street. Two obelisks and a pyramid are in the background.

The Death Angel Passes Over an Israelite Door Marked with the Blood of a Lamb

"And the blood shall be to you for a token upon the houses where ye are: and when I see the blood, I…

"And they heard a great voice from heaven saying unto them, Come up hither. And they went up into heaven in the cloud; and their enemies beheld them." Revelation 11:12 ASV <p>Illustration of the two witnesses, or prophets, from Revelation being taken up into heaven in a cloud. One man has his hands clasped in a prayer position. Below them is a staircase, columns, pyramid, and trees.

The Two Witnesses Taken to Heaven in a Cloud

"And they heard a great voice from heaven saying unto them, Come up hither. And they went up into heaven…