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Browse College Polyhedra
Stars indicate particularly interesting answers or
good places to begin browsing.
 Definitions as a Tool of Mathematics [03/04/2003]

Defining polyhedra: regarding unusual polyhedra, how can we exclude
'doubled' shapes, e.g. two tetrahedra that join at a single vertex
(sort of like an hourglass)?
 Biggest Cuboid in a Sphere [03/20/2003]

I have a sphere with radius of 10cm. I have to find the biggest cuboid
that fits in that sphere.
 Calculating Angles Between Faces of a Solid [09/15/2003]

How can I compute the dihedral angles for a Great Rhombicosidodecahedron?
 Cylinders and Euler's Rule [09/06/2002]

How and why does Euler's rule work for cylinders?
 Euler's Formula for Polyhedra [08/12/1997]

How would you prove Euler's formula VE+F = 2 for all polyhedra of genus
zero?
 Faces, Vertices, and Edges of Cylinders, Cones, and Spheres [12/28/2003]

Do cylinders, cones and spheres have faces, vertices, and edges? I'm
not sure how they would fit into Euler's formula of v  e + f = 2.
 Finding the Area of an Irregular Polygon [02/23/2008]

What is the formula for finding the area of an irregular polygon?
 Finding the Area of an Irregular Polygon in 3D [02/04/2009]

Given the coordinates of eight points in threedimensional space, with
no known angles, how can I find the area of the polygon they define?
 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?
 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.
 HigherDimensional Cubes [07/04/2003]

I've written a program that draws cubes in any number of dimensions
between 0 and 15. I want to have it display the number of faces and
cells of each dimension each cube has.
 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?
 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 [1/31/1996]

What are the Platonic solids in 4 and more dimensions?
 Polyhedra: Solids or Surfaces? [06/06/2003]

Is a polyhedron always a solid figure?
 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?
 Spheres in a Cylinder [05/20/2003]

Spheres of 6 cm radius are dropped into a cylinder of radius 8 cm and
height 36 cm. How many spheres can fit into the cylinder?
 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?
 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?
 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 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 onethird 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.
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