




 Rotate a cube about an axis through opposite edges






 Folding up 6 pyramids to make a cube





 How to make a cube by folding up a net.






 click this icon on the right to access the net in a browser






 or download and open this Cabri 3D file: folding_cube.cg3





 Create a shape which will fold up into a cube using only one perpendicular line and some rotations. You can guide students to imagine the net of a cube out of a piece of paper. What transformations are needed to fold this up into a cube?





 Start with a square. Read the tool help instructions carefully to see what you need to select to create the square.





 Create a point Q and the segment PQ and then the circle with axis PQ passing through O. (Click a point and type a letter to label it.)





 Rotate the square about segment PQ : Choose PQ, ...





 ... then choose the square, ...





 ... then choose two points which have the required angle between them.





 The rotated image is formed.





 The new point on the circle is labelled R.





 Now the square with centre R is rotated about the vertical vector through O. Select this vector, ...





 ... then select the square, ...





 ... finally, select point P. (note that POQ defines a right angle in this case)





 This new square is then rotated similarly, and its image is also rotated.





 The vertical vector through O is extended into a line. The line perpendicular to the square with centre R and passing through point R is created. The intersection S of these two lines is found.





 The square with centre O is now reflected (central symmetry tool) in point S to create the final face of the cube. Select S.





 Alternatively, the square with centre O may be rotated about the perpendicular line through R to create the final face.





 Challenge: Use a similar technique, construct a fold up dodecahedron or icosahedron.





 Rotation, Cross sections and other explorations of Regular Dodecahedron






 inscribed with 3 other platonic solids






 mutually perpendicular edges highlighted






 golden rectangles inscribed






 cross sections parallel to a face






 cross sections parallel to an axis through midpoints of opposite edges.






 cross sections perpendicular to an axis through opposite vertices






 rotation about axis through centers of opposite faces






 rotation about axis through midpoints of opposite edges






 rotation about axis through opposite vertices






 Rotate a regular octahedron about an axis through midpoints of opposite edges.






 Net of a regular octahedron






 The same net but folded into another octahedron






 Truncate a polyhedron to make some Archimedean solids





 Other resources on Regular and Semiregular Solids








 construct lines and planes in a regular polyhedron






