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- 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 V-E+F = 2 for all polyhedra of genus
- 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 3-D [02/04/2009]
Given the coordinates of eight points in three-dimensional 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.
- Higher-Dimensional 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 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.