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High School Archive

Browse High School Polyhedra

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Finding the Height of a Tetrahedron [05/03/1998]

Using properties of medians, altitudes, and angle bisectors to find the height of a tetrahedron of equilateral triangles.

Find the Edge Lengths of a Cuboid [05/13/2003]

I am trying to discover the lengths of the edges of a cuboid when only the diagonal, area, and volume are known.

Geodesics [12/15/1996]

Can you give me information on the math behind geodesics?

Geometry and Soccer balls [10/29/1998]

I'm looking for ideas for a geometry and soccer bulletin board.

Height of Tetrahedral Pyramid [09/12/2001]

I'm looking for a simple formula (and derivation) of the height of a tetrahedral pyramid with an equilateral triangle as a base.

Hidden Faces in a Set of Cubes [10/04/2000]

Can you give us a hint for a formula that will tell you the number of hidden faces in an arrangement of a cubes if you know the number of visible faces?

How Many Pyramids? [08/21/2003]

If a pyramid is 2 feet tall, and crumbles into sand, how many 2-inch pyramids can be created from the sand used to create the original pyramid?

How Many Rectangular Solids in a Cube? [09/13/2001]

Is there any standard way of finding out how many different possible rectangular solids can fit into an 3^3 cube?

Importance of Surface Area [05/26/2001]

Why is surface area so important? What kinds of things depend on surface area?

KaleidoTile [11/15/1995]

I would appreciate it if you would tell me a bit about KaleidoTile.

Length of a Line Segment in Three Dimensions [04/16/2004]

What is the length of a line segment in three dimensions with endpoints (1, 0, 2) and (1, 4, 5)?

Maximizing the Volume of a Box [06/27/1999]

I have a piece of glass that is 14" by 72". What dimensions would I need to make a glass cage with maximum volume?

Maximizing Volume of a Cereal Box [07/08/1999]

Why are cereal boxes the size they are? Is it just to maximize volume?

Maximum Area of a Rectangle with Fixed Perimeter [03/03/2004]

If I am given a specific length of fence, such as 128 feet, how can I calculate the maximum amount of square footage that I can enclose in a rectangle using the fence?

Maximum Surface Area for Total Edge Length [07/14/2002]

A piece of wire of total length L units is used to form the nine edges of a prism whose ends are equilateral triangles and whose other faces are rectangles. What is the maximum surface area of this prism?

Mitres on Pyramids [09/26/2002]

I am weatherproofing my home, and have to mitre boards in a pyramid with a rectangular - not square - base, and an apex that is directly over the centre of one edge of the base.

Monogons and Digons - Polygons with Fewer Than 3 Sides [01/24/2006]

What do monogon and digon polygons look like? How can you have a polygon with fewer than three sides?

Net of a Box [05/23/1999]

Choose dimensions (length, width, and height) and find the surface area and volume of a box; then draw a flat pattern of the box.

Nets in a Geometrical Sense [03/07/1999]

What is the "net" of a shape?

Numbering the Faces of Dice [02/27/2001]

How many ways are there to make dice out of the Platonic solids (i.e. 4, 6, 8, 12, and 20 sides)? How many of those ways have opposite face sums equal? What would the opposing face sums be for each type?

Open Box Problem [06/22/2003]

Find the formula for the greatest volume box you can make from a sheet of cardboard with different-sized corners cut out of it.

Orbit and Stabilizer in Rotational Symmetry [11/11/2004]

Calculate the orders of the following groups of rotations: of a regular tetrahedron, a regular octahedron, a regular dodecahedron, and a regular icosahedron. I'm having trouble figuring out the stabilizers. I know that the order of the group of rotations is equal to the order of the orbit times the order of the stabilizer.

Orthocentric Tetrahedron [11/30/2002]

Recall that the opposite edges of an orthocentric tetrahedron are perpendicular. Let ABCD be an orthocentric tetrahedron. Show that AB^ 2 + CD^2 = AD^2 + BC^2.

Platonic Solids [01/01/1997]

Is there such a thing as a regular 7-hedron?

Pole in a Box [02/09/1999]

Can a pole 6.5m long fit into a truck with dimensions of 3m, 3.5m, and 4m?

Polyhedra: Classification, Theorem [02/12/1998]

I would like to know how polyhedrons are classified, which figures can be used for the faces, and the theorem relating the faces, edges, and vertices.

Polyhedron inside Sphere [5/24/1996]

How long do the sides of a dodecahedron have to be to fit into a sphere of diameter 2.9 m?

Polyhedron Problem [10/29/1996]

How many faces share each edge?

Polyhedron Project [10/29/2003]

I'd like to do a project involving tetrahedra. What would you suggest?

Polyhedron Vertices [02/25/2003]

What is the least number of vertices that a polyhedron may have?

Pyramids and Triangular Prisms [05/09/2000]

What's the difference between a pyramid and a triangular prism?

Pythagorean Theorem and Cubes [02/14/1998]

In a cube if a diagonal is drawn from the front top corner to the back bottom corner, how long must each side be using the Pythagorean Theorem?

Pythagorean Theorem in Three Dimensions [05/18/2001]

Given a tetrahedron with a trirectangular vertex S. Let A, B, and C be the areas of the three faces that meet at S, and D be the area of the face opposite S. Prove that D^2 = A^2 + B^2 + C^2.

Rectangular Solids from Blocks [09/25/1998]

How many rectangular solids can be made from "n" cube-shaped blocks?

Rhombicuboctahedron [05/14/1999]

How can you make a soccer ball out of a particular shape - for example the rhombicuboctahedron?

Snub Cube [08/08/1998]

What is a snub cube?

The Spider and the Fly [12/23/1999]

A spider and a fly are on opposite walls of a rectangular room... Does the spider get the fly?

Spiral Inside a Hexagonal Room [09/03/2003]

Two walls meet at 120 degrees, and you have a piece of cardboard with an angle of 137.5 degrees that you want to tilt until its sides are snug against the wall. How do you find the angle of tilt?

Stella Octangula [6/17/1996]

What is the name of the polyhedron that looks like the union of two tetrahedrons joined at their bases?

Stellated Dodecahedron [12/3/1995]

A student asks for help finding information on stellated dodecahedrons.

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