ClipArt images of uncommon 3-dimensional figures including hexahedrons, diploids, tetrahexahedrons, and more.

An arch

Arch

An arch

Isometric of a wooden block.

Isometric of a Block

Isometric of a wooden block.

Isometric of a wooden brace.

Isometric of a Brace

Isometric of a wooden brace.

Projection of a circular ring.

Projection of Circular Ring

Projection of a circular ring.

An illustration of a composite figure made up of a quadrilateral frustum and half of a cylinder. Frustum edges range between 6 feet and 11 feet 5 inches and cylinder has a height of 12 feet.

Composite Figure of Quadrilateral Frustum With Half of a Cylinder Attached

An illustration of a composite figure made up of a quadrilateral frustum and half of a cylinder. Frustum…

Illustration used to compare the volumes of a cone and a cylinder by emptying sand from the cone into the cylinder.

Comparative Volumes Of A Cone And Cylinder

Illustration used to compare the volumes of a cone and a cylinder by emptying sand from the cone into…

Illustration used to compare the volumes of a cone, a sphere, and a cylinder.

Comparative Volumes Of A Cone, Sphere, And Cylinder

Illustration used to compare the volumes of a cone, a sphere, and a cylinder.

Illustration showing solid twin crystals.

Twin Crystals

Illustration showing solid twin crystals.

A cube (A) has sides of 20 inches in length each, making its solid contents equal 8000 cubic inches. Being added are 3 equal portions 20x20x5, equaling 2000 cubic inches. The sum of these are 6000. You can find the second portion of the problem <a href="../62392/62392_cube_add2.htm">here</a>.

Cube with Additions 1

A cube (A) has sides of 20 inches in length each, making its solid contents equal 8000 cubic inches.…

In order to fill in the spaces from the three 2000 cubic inch additions, four new additions must be added: three 20x5x5 bars equaling 500 cubic inches and a 5x5x5 (125 cubic inches) cube for the corner. You can find the final cube <a href="../62393/62393_cube_add3.htm">here</a>.

Cube with Additions 2

In order to fill in the spaces from the three 2000 cubic inch additions, four new additions must be…

This is the final form of the original 20x20x20 inch or 8000 cubic inch cube with the addition of 7625 cubic inches making it a 25x25x25 inch cube equaling 15,625 cubic inches. You can find the original cube <a href="../62391/62391_cube_add1.htm">here</a>.

Cube with Additions 3

This is the final form of the original 20x20x20 inch or 8000 cubic inch cube with the addition of 7625…

"A penetration twin, since the two individuals interpenetrate each other." &mdash; Ford, 1912

Twinned cubes

"A penetration twin, since the two individuals interpenetrate each other." — Ford, 1912

A solid with fourteen faces formed by cutting off the corners of a cube parallel to the coxial octahedron far enough to leave the original faces squares, while adding eight triangular faces at the truncations.

Cuboctahedron

A solid with fourteen faces formed by cutting off the corners of a cube parallel to the coxial octahedron…

Illustration used to compare the surfaces of a cylinder and a sphere.

Comparative Surfaces Of A Cylinder And Sphere

Illustration used to compare the surfaces of a cylinder and a sphere.

Illustration showing a deltohedron.

Deltohedron

Illustration showing a deltohedron.

Principal forms of the isometric system: deltohedron

Deltohedron

Principal forms of the isometric system: deltohedron

"A four-sided figure, formed of 2 unequal isosceles triangles on different sides of a common base." &mdash; Williams, 1889

Deltoid

"A four-sided figure, formed of 2 unequal isosceles triangles on different sides of a common base."…

"The diploid is a rare form found only in this class. It is composed of twenty-four faces which correspond to one-half the faces of a hexoctahedron." &mdash; Ford, 1912

Diploid

"The diploid is a rare form found only in this class. It is composed of twenty-four faces which correspond…

A solid belonging to the isometric system, with 24 trapezoidal planes. It is the parallel hemihedral form of the hexoctahedron.

Diploid

A solid belonging to the isometric system, with 24 trapezoidal planes. It is the parallel hemihedral…

"A combination of cube and diploid." &mdash; Ford, 1912

Diploid and cube

"A combination of cube and diploid." — Ford, 1912

A gable

Gable

A gable

A 1/2 gable

Half Gable

A 1/2 gable

An illustration of a prismatoid with circular base.

Geometric Solid with Circular Base

An illustration of a prismatoid with circular base.

Principal forms of the triclinic system: hemi-brachy dome.

Hemi-brachy Dome

Principal forms of the triclinic system: hemi-brachy dome.

Hexahedron - polyhedron with 6 faces.

Hexahedron

Hexahedron - polyhedron with 6 faces.

Hexahedron - polyhedron with 6 faces.

Hexahedron

Hexahedron - polyhedron with 6 faces.

Hexahedron with faces and vertices shown.

Hexahedron With Faces and Vertices

Hexahedron with faces and vertices shown.

"Here each face of the octahedron is replaced by six scalene triangles, so that altogether there are fourty-eight faces. This is the greatest number of faces possible for an simple form in crystals." -The Encyclopedia Britannica 1910

Hexakis-octahedron

"Here each face of the octahedron is replaced by six scalene triangles, so that altogether there are…

"The hemihedral form {hkl} of the hexakis-octahedron; it is bounded by twenty-four scalene triangles and is the general form of the class." -The Encyclopedia Britannica 1910

Hexakis-tetrahedron

"The hemihedral form {hkl} of the hexakis-octahedron; it is bounded by twenty-four scalene triangles…

A fourty-eight sided geometric shape.

Hexakisoctahedron

A fourty-eight sided geometric shape.

"The faces of the hexakistetrahedron correspond to one-half the faces of the hexoctahedron." &mdash; Ford, 1912

Hexakistetrahedron

"The faces of the hexakistetrahedron correspond to one-half the faces of the hexoctahedron." —…

"The hexoctahedron is a form composed of forty-eight triangular faces, each of which cuts differently on all three crystallographic axes. There are several hexoctahedrons, which have varying ratios of intersection with the axes." &mdash; Ford, 1912

Hexoctahedron

"The hexoctahedron is a form composed of forty-eight triangular faces, each of which cuts differently…

Illustration showing a hexoctahedron.

Hexoctahedron

Illustration showing a hexoctahedron.

Principal forms of the isometric system: hextetrahedron.

Hextetrahedron

Principal forms of the isometric system: hextetrahedron.

Isometric outline of a house.

Isometric of a House

Isometric outline of a house.

Illustration of an icosahedron.

Icosahedron

Illustration of an icosahedron.

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,…

"Bounded by twenty-four trapezoidal faces, and hence somethings called a 'trapezohedron.'" -The Encyclopedia Britannica 1910

Icositetrahedron

"Bounded by twenty-four trapezoidal faces, and hence somethings called a 'trapezohedron.'" -The Encyclopedia…

"Here one cube may be brought into the position of the other by a rotation of 180 degrees about a traid axis, or by reflection across the octrahedral plane which is perpendicular to this axis." -The Encyclopedia Britannica 1910

Interpenetrating Twinned Cubes

"Here one cube may be brought into the position of the other by a rotation of 180 degrees about a traid…

Illustration showing a general way the method of arranging the triangles on the irregular surface of solids is done.

Practical Projection Of An Irregular Solid

Illustration showing a general way the method of arranging the triangles on the irregular surface of…

"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…

"A contact twin, since the two individuals lie simply in contact with each other upon a certain plane." &mdash; Ford, 1912

Twinned octahedron

"A contact twin, since the two individuals lie simply in contact with each other upon a certain plane."…

"general form...bounded by four scalene triangles." -The Encyclopedia Britannica 1910

Orthorhombic Bisphenoid

"general form...bounded by four scalene triangles." -The Encyclopedia Britannica 1910

"This is the only simple form in this class which differs geometricalled from those of the holosymmetric class...These are each bounded by twenty-four irregular pentagons, and althrough similar to each other they are respectively right- and left-handed..." -The Encyclopedia Britannica 1910

Pentagonal Icositetrahedron

"This is the only simple form in this class which differs geometricalled from those of the holosymmetric…

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.

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases connected by an alternating band of triangles and trapezoids, unlike an antiprism that has an alternating band of only triangles.

Polyhedron With Pentagon Bases

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases…

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases connected by an alternating band of triangles and trapezoids, unlike an antiprism that has an alternating band of only triangles.

Polyhedron With Pentagon Bases

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases…

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases connected by an alternating band of triangles and trapezoids, unlike an antiprism that has an alternating band of only triangles.

Polyhedron With Pentagon Bases

Illustration of a pentagonal polyhedron that is formed by having two parallel congruent pentagonal bases…

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

Regular Polyhedrons

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

Two similar polyhedrons may be decomposed into the same number of tetrahedrons similar, each to each, and similarly placed.

Similar Polyhedrons

Two similar polyhedrons may be decomposed into the same number of tetrahedrons similar, each to each,…

A solid having two parallel polygonal bases connected by triangular faces.

Prismatoid

A solid having two parallel polygonal bases connected by triangular faces.

Illustration of a plane passing through a prismatoid.

Plane Passing Through Prismatoid

Illustration of a plane passing through a prismatoid.

An illustration of a prismatoid with faces that are quadrilaterals.

Prismatoid With Quadrilateral Faces

An illustration of a prismatoid with faces that are quadrilaterals.

An illustration of a prismatoid with triangular faces and points labeled.

Prismatoid With Triangular Faces

An illustration of a prismatoid with triangular faces and points labeled.

Illustration to show how volume of a prismatoid is found. "The volume of a prismatoid is equal to the product of one sixth of its altitude into the sum of its bases and four times its mid-section." V=1/6H(B+b+4M)

Prismatoid Illustration for Volume

Illustration to show how volume of a prismatoid is found. "The volume of a prismatoid is equal to the…

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…

Principal forms of the isometric system: pyritohedron.

Pyritohedron

Principal forms of the isometric system: pyritohedron.