Example A Truncated Pyramid Cut by Prism Additional

Example A: Truncated Pyramid Cut by Prism 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 A: Truncated Pyramid Cut by Prism S‘‘ A straight pyramid with a regular hexagonal basement is truncated by plane σ of second edge view, 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 prism. This prism 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 prism. f‘‘ Define points A 1, B 1, D 1 and E 1 in the plan view. D 1‘‘ =E 1‘‘ These points are points on according edges AS, BS, DS and ES. A 1‘‘ =B 1‘‘ s‘‘ C‘‘ = F‘‘ A‘‘ = B‘‘ D‘‘ =E‘‘ 30 20 s‘ A‘ E‘ A 1‘ E 1‘ q 10 5 70 F‘ z S‘ f‘ D 1‘ y 40 80 B‘ B 1‘ D‘ C‘ x 2

Example A: Truncated Pyramid Cut by Prism S‘‘ A straight pyramid with a regular hexagonal basement is truncated by plane σ of second edge view, 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 prism. This prism 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 prism. Locate points C 2 and F 2 in the plan view- use level plane, which intersects the pyramid along a similar hexagon. f‘‘ D 1‘‘ =E 1‘‘ C 2‘‘ =F 2‘‘ A 1‘‘ =B 1‘‘ The top face of the truncated pyramid is defined. s‘‘ F 2‘ s‘ 30 20 70 F‘ A‘ E‘ A 1‘ E 1‘ q 10 5 Show the visible remaining part of the edges of the pyramid through A, B, D and E. D‘‘ =E‘‘ C‘‘ = F‘‘ A‘‘ = B‘‘ z S‘ f‘ D 1‘ y 40 80 B‘ B 1‘ D‘ C 2‘ C‘ x 3

Example A: Truncated Pyramid Cut by Prism S‘‘ A straight pyramid with a regular hexagonal basement is truncated by plane σ of second edge view, 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 prism. This prism 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 prism. f‘‘ Determine intersection lines of the intersection of prism with top surface. D 1‘‘ =E 1‘‘ C 2‘‘ =F 2‘‘ A 1‘‘ =B 1‘‘ Show proper visibility of remaining part of the top surface. s‘‘ D‘‘ =E‘‘ C‘‘ = F‘‘ A‘‘ = B‘‘ s‘ 30 20 F 2‘ A‘ E‘ A 1‘ E 1‘ q 10 5 70 F‘ z S‘ f‘ D 1‘ y 40 80 B‘ B 1‘ D‘ C 2‘ C‘ x 4

Example A: Truncated Pyramid Cut by Prism S‘‘ A straight pyramid with a regular hexagonal basement is truncated by plane σ of second edge view, 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 prism. This prism 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 prism. Locate points C 1 and F 1 in the plan view. Use level plane, which intersects the pyramid along similar hexagon. f‘‘ D 1‘‘ =E 1‘‘ C 2‘‘ =F 2‘‘ A 1‘‘ =B 1‘‘ C 1‘‘ =F 1‘‘ s‘‘ C‘‘ = F‘‘ A‘‘ = B‘‘ D‘‘ =E‘‘ F‘ 30 20 s‘ A‘ E‘ A 1‘ E 1‘ q 10 5 70 F 1‘ F 2‘ z S‘ f‘ D 1‘ y 80 B‘ B 1‘ D‘ C 2‘ C 1‘ 40 C‘ x 5

Example A: Truncated Pyramid Cut by Prism S‘‘ A straight pyramid with a regular hexagonal basement is truncated by plane σ of second edge view, 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 prism. This prism 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 prism. f‘‘ D 1‘‘ =E 1‘‘ Use auxiliary plane of second edge view through lateral face of prism to define further intercepts of the intersection polygon. C 2‘‘ =F 2‘‘ A 1‘‘ =B 1‘‘ C 1‘‘ =F 1‘‘ s‘‘ C‘‘ = F‘‘ A‘‘ = B‘‘ D‘‘ =E‘‘ F‘ 30 20 s‘ A‘ E‘ A 1‘ E 1‘ q 10 5 70 F 1‘ F 2‘ D 1‘ z S‘ f‘ D 1‘ y 80 B‘ B 1‘ D‘ C 2‘ C 1‘ 40 C‘ x 6

Example A: Truncated Pyramid Cut by Prism S‘‘ A straight pyramid with a regular hexagonal basement is truncated by plane σ of second edge view, 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 prism. This prism 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 prism. f‘‘ D 1‘‘ =E 1‘‘ Define the intersection polygon and show proper visibility. C 2‘‘ =F 2‘‘ A 1‘‘ =B 1‘‘ C 1‘‘ =F 1‘‘ s‘‘ C‘‘ = F‘‘ A‘‘ = B‘‘ D‘‘ =E‘‘ F‘ 30 20 s‘ A‘ E‘ A 1‘ E 1‘ q 10 5 70 F 1‘ F 2‘ z S‘ f‘ D 1‘ y 80 B‘ B 1‘ D‘ C 2‘ C 1‘ 40 C‘ x 7