In the 1980's Rubik's cube was so popular that it was simply called "the cube".
The ratio depends on the angles of the sloping lines. The three following statements produce good pictures: The mathematical base is the "sloping parallel projection", where all ratios and angles are possible. You choose simple angles and simple ratios (Book S). There is Pohlke's theorem (also called "Main theorem of the axonometry"):
More Cubes in Perspective Central Projection
Nets of a Cube
Stereogram You can see the cube three-dimensionally in the following picture. Shadow pictures of a rotating cube
Model with edges There are different methods of building cubes with rods.
More exact: There are building kits, which use 12 straws and 8 tripods
of plastic (One red tripod is removed below in the photo).
You can find 13 rotation axes. If you turn around one of these axes, the cube goes back to itself. The following picture illustrates these facts. The numbers under the cubes indicate the number of turns.
All spatial diagonals Cube with cut corners Cut the corners of a cube. Divide the edges in three equal pieces to do this. You get a body formed by 6 octogons and 8 equilateral triangles. Cuboctahedron Cut the corners of a cube. Take half the edges. You get a body formed by 6 squares and 8 equilateral triangles. . Tetrahedron in the cube Draw some square diagonals and you get a tetrahedron. Octahedron in the cube Join the centres of the squares by lines. You get an octahedron. More: If you join the centres of the triangles of a octahedron, a cube develops again. Cube and octahedron are dual to each other. Three pyramids of equal volumes The largest square inside
a cube
The red square is the largest square which fits a cube.
Cube in the cube
The red cube is the smallest cube which touches all sides of the black cube (more on web page E). Hexagon inside a cube Join centres of some edges. You get an intersection through the cube.
A spatial equilateral hexagon
There are many puzzles based on polycubes. Here is my "hit list": I describe the puzzles on other places of my homepage. There are 1
Soma
cube, 2 Mac Mahons Coloured Cubes, 3
Rubik's
cube, 4
Happy Cube, and 5 Origami
cube.
Well known illusions with cubes are "tilt figures". I restrict on them.
You have the questions: Right or left? From below or above? Three or five cubes? Five or three cubes? How many cubes? The five pictures above are ambiguous. You see the cube from below or
above.
Do you look on a tower or into a hole?
1 The T-Digit of the "Deutsche Telekom" was a centre of the exhibition
area. You could look at a large screen sitting on the steps of show stairs
where (even in the sunshine) an impressive light TV picture was to be seen.
Have a look at the French Open in Paris.
German H. B. Meyer (Polyeder aus Flechtstreifen)
Richard Mischak
Wikipedia
English David Eppstein (Geometry Junkyard)
Eric Weisstein (MathWorld)
H. B. Meyer (Polyeder aus Flechtstreifen)
Henry Bottomley
Jim Loy
Wikipedia
Feedback: Email address on my main page
This page is also available in German. URL of
my Homepage:
© 2002 Jürgen Köller |