# Construct a line of intersection of a pyramid with a direct prism

In the section Crossing polyhedra to the polyhedra often used in practice, one can include a prism and a pyramid. We will accomplish several tasks at the intersection of the pyramid and the prism.

In this task on descriptive geometry it is necessary to construct a line of intersection of a pyramid with a direct prism.

Given:

Projections of the pyramid and prism

Option | Table of values of the coordinates of points and height h of the prism | ||||||||||||

1 | X_{A} |
Y_{A} |
Z_{A} |
X_{B} |
Y_{B} |
Z_{B} |
X_{C} |
Y_{C} |
Z_{C} |
X_{D} |
Y_{D} |
Z_{D} |
X_{E} |

141 | 75 | 0 | 122 | 14 | 77 | 87 | 100 | 40 | 0 | 50 | 40 | 100 | |

Y_{E} |
Z_{E} |
X_{K} |
Y_{K} |
Z_{K} |
X_{G} |
Y_{G} |
Z_{G} |
X_{U} |
Y_{U} |
Z_{U} |
h | ||

50 | 0 | 74 | 20 | 0 | 16 | 20 | 0 | 55 | 95 | 0 | 85 |

The solution of problems on descriptive geometry I produce in the automated design system AutoCAD and AutoCAD 3D. This training will allow you to develop spatial thinking and consolidate the possession of AutoCAD.

## Solution of the problem of intersection of a pyramid and a prism

The solution to the problem of intersection of a pyramid and a prism is simplified by the fact that the prism of its base is on the level plane, and the horizontal projections of its vertical edges are transformed into points. The edges of the lateral surface of the prism are the compartments of horizontally projecting planes.

- We construct the projections of the pyramid and the prism. The values of the coordinates of the points are taken from the table of the values of the coordinates.
- The lines of intersection of a pyramid with a direct prism are determined from the points of intersection of the edges of each of them with the faces of another polyhedron or by constructing the line of intersection of the faces of the polyhedron. By connecting each pair of such points of the same faces by straight lines, we construct a line of intersection of the pyramid with a straight prism.
- Visible are only those sides of the intersection polygon that belong to the visible faces of the polyhedra. In more detail in the video tutorial on descriptive geometry.

## Video "Crossing the Pyramid and Prism (Russian)"

This video tutorial and article are included in the professional free self-instruction manual AutoCAD, which is suitable for both novice users and those already working in AutoCAD.

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