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High School Archive

Browse High School Polyhedra

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Surface Area and Volume: Cubes and Prisms [05/27/1998]

What is the definition of surface area and volume? What are the differences and similarities between surface area and volume?

Surface Area of a Rectangular Solid [09/21/1999]

Can you find the surface area of a cube or other 3D rectangular object by calculating the area of the sides you can see and multiplying by 2?

Surface Area of Blocks Glued Together [09/09/2001]

Three cubes whose edges are 2, 6, and 8 centimeters long are glued together at their faces. Compute the minimum surface area possible for the resulting figure.

Surface Area of Pyramids [05/21/1999]

We understand how to find the surface area, but we cannot figure out how to determine the slant.

Surface Area Of Three Cubes Glued Together [10/22/2002]

You have 3 cubes, one with an edge measuring 2, one 6, and one 8. If you glue them together so you have the smallest possible surface area, what will that surface area be?

Symmetry in Platonic Solids [01/24/1997]

How many planes of symmetry does each of the platonic solids have?

Tetrahedron Projected on a Plane [10/29/1996]

How do you project a regular tetrahedron perpendicularly onto a plane to get the maximum area shadow?

Triangle Proportions: A Diagram [05/06/2003]

A cone has a circular base radius 1, and vertex of height 3 directly above the center of the circle. A cube has four vertices in the base and four on the sloping sides. What is the length of a side of the cube?

Truncating Platonic Solids [08/04/1998]

What effect does truncation have on Platonic solids? What are some historical and current applications?

Types of Pyramids [06/08/1999]

What are the types of pyramids and what do they look like?

Understanding Fourth Dimension Figures [07/05/1998]

Can you help me figure out the equations for fourth dimension figures such as the tesseract and the hypertetrahedron?

Volume of a Frustum of a Pyramid [06/03/2002]

How can I derive the formula for the volume of a frustum of a pyramid?

Volume of a Pyramid [05/29/2002]

Why does the formula for the volume of pyramid have a 1/3 in it?

Volume of a Regular Octahedron [09/12/2004]

How do you find the volume of a regular octahedron if you don't know the height?

Volume of a Rhombicuboctahedron [01/19/2001]

What is the formula for finding the volume of a polyhedron called a rhombicuboctahedron?

Volume of a Soccer Ball [05/31/2003]

What is the simplest way to find the volume of a truncated icosahedron (aka soccer ball or buckyball)?

Volume of a Tetrahedron [01/23/2002]

The volume of a tetrahedron is one-third the distance from a vertex to the opposite face, times the area of that face. Find a formula for the volume of a tetrahedron in terms of the coordinates of its vertices P, Q, R, and S.

Volume of a Tetrahedron [02/27/2003]

Find the volume of a tetrahedron.

What Does "Stellated" Mean? [03/31/1998]

Stellating polyhedra, including solids that are already stellated.

What is a Cuboctahedron? [01/02/2001]

What is a cuboctahedron?

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