From ProofWiki
Jump to navigation Jump to search



Let $P$ be a polygon.

Let $Q$ be a point not in the plane of $P$.

From each vertex of $P$, let lines be drawn to $Q$.

The polyhedron which is contained by $P$ and the triangles formed by the sides of $P$ and the lines to $Q$ is a pyramid.

In the words of Euclid:

A pyramid is a solid figure, contained by planes, which is constructed from one plane to one point.

(The Elements: Book $\text{XI}$: Definition $12$)

Apex of Pyramid

The vertex of a pyramid which is the common vertex of its triangular faces is called the apex of the pyramid.

In the above diagram, $Q$ is the apex.

Base of Pyramid

The polygon of a pyramid to whose vertices the apex is joined is called the base of the pyramid.

In the above diagram, $ABCDE$ is the base of the pyramid $ABCDEQ$.

Lateral Face of Pyramid

The triangular faces of a pyramid which lead to the apex are called the lateral faces of the pyramid.

In the above diagram, $ABQ$ and $DEQ$, for example, form two of the $5$ lateral faces of the pyramid $ABCDEQ$.

Lateral Edge of Pyramid

The lateral edges of a pyramid are the edges which join the vertices of the lateral faces.

In the above diagram, the edges $AQ, BQ, CQ, DQ$ and $EQ$ are the lateral edges of the pyramid.

Height of Pyramid

The height of a pyramid is the length of the perpendicular from the plane of the base to its apex.

In the above diagram, $h$ is the height.

Also see

  • Results about pyramids can be found here.

Linguistic Note

The word pyramid derives directly from the Classical Greek πυραμίς (pyramis) whose derivation is unknown.

In natural language the word usually refers to a square pyramid, and usually calls to mind the Great Pyramid of Giza.