Example Intersection of Truncated Pyramid and Cuboid Additional

Example: Intersection of Truncated Pyramid and Cuboid 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: Intersection of Truncated Pyramid and Cuboid A straight pyramid with a hexagonal basement is truncated by plane σ, which is given by line f and its intersection line s with the basement´s plane. The remaining truncated surface of the pyramid is further cut by a horizontal straight cuboid. This cuboid is given by its cross section, which is a square in a symmetrical plane of the pyramid. Define the intersection polygon of the truncated pyramid and the cuboid. S Show proper visibility of the remaining surface. Define the truncated pyramid: Use a vertical plane of symmetry of the pyramid, which contains the cross section of the horizontal cuboid. f E F s D C M A f‘ B 2

Example: Intersection of Truncated Pyramid and Cuboid A straight pyramid with a hexagonal basement is truncated by plane σ, which is given by line f and its intersection line s with the basement´s plane. The remaining truncated surface of the pyramid is further cut by a horizontal straight cuboid. This cuboid is given by its cross section, which is a square in a symmetrical plane of the pyramid. Define the intersection polygon of the truncated pyramid and the cuboid. S Show proper visibility of the remaining surface. Define the truncated pyramid: Use a vertical plane of symmetry of the pyramid, which contains the cross section of the horizontal cuboid. f Define the intersection line of the plane of symmetry and the skew plane to determine the top face of the truncated pyramid. E F s D C M A f‘ B 3

Example: Intersection of Truncated Pyramid and Cuboid A straight pyramid with a hexagonal basement is truncated by plane σ, which is given by line f and its intersection line s with the basement´s plane. The remaining truncated surface of the pyramid is further cut by a horizontal straight cuboid. This cuboid is given by its cross section, which is a square in a symmetrical plane of the pyramid. Define the intersection polygon of the truncated pyramid and the cuboid. S Show proper visibility of the remaining surface. Construct the horizontal cuboid by extruding its cross section and define intercepts with the lateral faces of the pyramid. f E F s D C M A f‘ B 4

Example: Intersection of Truncated Pyramid and Cuboid A straight pyramid with a hexagonal basement is truncated by plane σ, which is given by line f and its intersection line s with the basement´s plane. The remaining truncated surface of the pyramid is further cut by a horizontal straight cuboid. This cuboid is given by its cross section, which is a square in a symmetrical plane of the pyramid. Define the intersection polygon of the truncated pyramid and the cuboid. S Show proper visibility of the remaining surface. Define proper visibility for remaining edges of the truncated surface. f E F s D C M A f‘ B 5

Example: Intersection of Truncated Pyramid and Cuboid A straight pyramid with a hexagonal basement is truncated by plane σ, which is given by line f and its intersection line s with the basement´s plane. The remaining truncated surface of the pyramid is further cut by a horizontal straight cuboid. This cuboid is given by its cross section, which is a square in a symmetrical plane of the pyramid. Define the intersection polygon of the truncated pyramid and the cuboid. S Show proper visibility of the remaining surface. Extrude the cross section of the cuboid to define intercepts on edge BS and ES. Use an auxiliary plane through one side of the cuboid to define further intercepts. f E F s D C M A f‘ B 6

Example: Intersection of Truncated Pyramid and Cuboid A straight pyramid with a hexagonal basement is truncated by plane σ, which is given by line f and its intersection line s with the basement´s plane. The remaining truncated surface of the pyramid is further cut by a horizontal straight cuboid. This cuboid is given by its cross section, which is a square in a symmetrical plane of the pyramid. Define the intersection polygon of the truncated pyramid and the cuboid. S Show proper visibility of the remaining surface. Connect all points of the intersection polygon. Show proper visibility of the remaining SURFACE. f E F s D C M A f‘ B 7