See also the
Dr. Math FAQ:
3D and higher
Browse Middle School Polyhedra
Stars indicate particularly interesting answers or
good places to begin browsing.
- How Many Cube Faces Were Painted? [02/23/2003]
Some unit cubes are put together to form a larger cube. Some of the
larger cube's faces are painted and then it is taken apart. 45 small
cubes are found to have no paint on them. How many faces of the large
cube were painted?
- Painting Cubes [01/06/2003]
How many unit cubes would be needed to create a cube with a side
length of 3 units? If you painted the larger cube and broke it up
into unit cubes, how many faces of each unit cube would be painted?
- A 78- or 79-Sided Polygon/Polyhedron [3/13/1995]
Is it possible to produce a 78- or 79-sided polygon or polyhedron, and if so, what would it look like?
- Bases and Faces [12/05/2001]
I can't figure out the difference between a base and a face on the shapes
we are learning.
- Classifying Quadrilaterals [01/25/2006]
How can a square also be a rectangle?
- Creating a Nine-Sided Polyhedron [12/9/1995]
We found the heptahedra picture, but we can't find out if a nine-faced
polyhedron can be made. Do you know where we could find a picture of it
if it can be made?
- Cube Edges [04/01/1997]
How many edges does a cube have?
- Cube Slicing [9/1/1995]
You are given a 3-inch cube that is painted red. This cube is in 27 one-
inch cubes. What is the number of cubes with red paint on them for 3, 4,
5, 6,...n inches? For 0 faces respectively we get 8, 27, 64, 150. These
are not proportional for each 1-inch increase in the 3-inch cube. How do
you figure the number of cubes with red paint on the cube of n-inches for
- Cups and Volume [12/06/2001]
How can I calculate the volume of a box, if I know how many cups of rice
fill it? And how can 2 cups be a volume measure?
- Cutting a Cube [07/05/1999]
How many pieces will there be if you make every (flat) slice through a
cube that goes through exactly three of the cube's corners - no more and
- Definitions of Cones and Cylinders [03/02/2004]
Are cones and cylinders pyramids, prisms or neither? My 5th grade
geometry class cannot reach an agreement on this subject!
- Dimensions of a Cardboard Box [09/28/1997]
A box with a square bottom and a volume of 2000 centimeters can be made
by cutting 5-centimeter squares from the corners of a piece of
- Edge of a Cube Given Volume [10/06/1997]
I am a teacher currently teaching volume to a class of Grade 5 pupils.
- Edges, Vertices, Surfaces [04/22/2003]
How can a shape have 8 edges and 5 vertices? How can a shape have 12
edges, all the same length? How can a shape have 3 surfaces, one
- Eleven Nets of a Cube [11/15/2001]
My teacher says that there are 11 combinations to make a cube without
reversing them, but I can only find 6.
- Euler's Formula [11/26/2001]
I have to find Euler's formula for two-dimensional figures and explain it
at a university level and at an elementary-school level.
- Far Side of the Cube? [03/08/2017]
Given the net of a cube, how do you figure out the opposite of any side? Doctor Peterson admits
that it takes practice to visualize three dimensions in two, then outlines how to build
the net of a cube — and label its edges for easy identification.
- Find Depth of Water in a Tank [08/02/2003]
A rectangular tank measures 4m long, 2m wide and 4.8m high. Initially
it is half full of water. Find the depth of water in the tank after
4000 litres of water have been added to it.
- Finding Area and Volume [04/12/2001]
When working with area and volume of triangular shapes, how do I know
when to divide the base by 2 and when to divide it by 3?
- Finding Surface Areas [06/17/2002]
Can you explain how to find the surface areas of solids?
- Finding the Dimensions of a Box [10/21/2001]
You want to construct a cardboard box from a cardboard strip that is 8
inches wide. The dimensions of the box are 8"x8"x4". How long does the
strip need to be?
- Geometry and Soccer balls [10/29/1998]
I'm looking for ideas for a geometry and soccer bulletin board.
- 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
- Importance of Surface Area [05/26/2001]
Why is surface area so important? What kinds of things depend on surface
- 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?
- Minimum Distance [5/22/1995]
Inside a rectangular room a spider is at a point on the middle of one of
the end walls and a fly is on the opposite wall. What is the shortest
distance the spider must crawl to reach the fly?
- 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.
- Net of a Hexagonal Pyramid [02/05/2001]
How would you draw the nets of a hexagonal pyramid and a rectangular
- Nets in a Geometrical Sense [03/07/1999]
What is the "net" of a shape?
- Origin of the Word Pyramid [07/05/1999]
Were the Egyptian pyramids named after the geometric figure 'pyramid' or
- Pole in a Box [02/09/1999]
Can a pole 6.5m long fit into a truck with dimensions of 3m, 3.5m, and
- 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
- Polyhedra - Sides? Faces? [10/13/1997]
How many sides do a tetrahedron and an icosahedron have?
- Polyhedron Vertices [02/25/2003]
What is the least number of vertices that a polyhedron may have?
- Prefixes for Naming Polyhedra [12/07/2000]
I am having trouble understanding Prof. Conway's explanation of his
system of prefixes for naming large numbers and polyhedra.
- Pyramid Corners [05/01/2001]
How many corners does a pyramid have? Is a corner the same thing as a
- Pyramids and Triangular Prisms [05/09/2000]
What's the difference between a pyramid and a triangular prism?
- Real World Polyhedra [6/4/1996]
Can you give me some information about the practical use of polyhedra?
- Rectangular Solids from Blocks [09/25/1998]
How many rectangular solids can be made from "n" cube-shaped blocks?
- Six Lines, 4 Triangles [8/19/1996]
How can you form four triangles from six toothpicks?