Example Octahedron by Bisection Part of a Cube

Example: Octahedron by Bisection – Part of a Cube Additional Task to the multimedia book „Darstellende Geometrie/ 3 D-Geometry“, published by Veritas Educational Edition Student Edition ISBN - 978 -3 -7058 -9079 -4 ISBN - 978 -3 -7058 -9293 -4 Special edition for teachers: The print version shows handouts of theory and worked-out examples. Each handout can be printed in colour and is also suitable as a solutions handout. Through the use of animated Power. Point files it is possible to structure the lessons in a contemporary and innovative manner for students. Special edition for students: The print version consists of well prepared worksheets to start working right away. On the CD you will find colourful Power. Point presentations, including theory as well as solved examples with step-by-step explanations. This provides a highly efficient technique in developing an understanding of geometry and its concepts. for more DETAILS and ORDER 1

Example: Octahedron by Bisection – Part of a Cube Construct the perspective view of an octahedron as a dual of a the given cube. Define the midpoint of each lateral face of the cube. Fx Fy z y x 2

Example: Octahedron by Bisection – Part of a Cube Construct the perspective view of an octahedron as a dual of a the given cube. Define the midpoint of each lateral face of the cube. Fx Fy z y x 3

Example: Octahedron by Bisection – Part of a Cube Construct the perspective view of an octahedron as a dual of a the given cube. Connect according points. Define the horizontal square of the octahedron. Fx Fy z y x 4

Example: Octahedron by Bisection – Part of a Cube Construct the perspective view of an octahedron as a dual of a the given cube. Verbinde die Quadrateckpunkte mit der oberen und mit der unteren Spitze. Berücksichtige die Sichtbarkeit. Fx Fy z y x 5

Example: Octahedron by Bisection – Part of a Cube Construct the perspective view of an octahedron as a dual of a the given cube. Connect the vertices of the square with the upper and lower apex. Show proper visibility. Fq Fx Fy z y x Genauigkeitskontrolle: Überprüfe, ob der Fluchpunkt zweier waagrechter Quadratkanten auf dem Horizont liegt. 6

Example: Octahedron by Bisection – Part of a Cube Construct the perspective view of an octahedron as a dual of a the given cube. Connect the vertices of the square with the upper and lower apex. Show proper visibility. Fq Fx Fy z y x Check your accuracy! Define the vanishing point Fg of two parallel horizontal edges of the octahedron. 7