6. Cross Sections
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Are all the surfaces flat? What does this tell us about whether or not it is a polyhedron? How many bases does the figure have?
| Solid | Base | Faces | Edges | Vertices |
|---|---|---|---|---|
| Hexagonal Pyramid | RQPONM | RQPONM, RQL, QPL, POL, ONL, NML, MRL | RQ, QP, PO, ON, NM, MR, RL, QL, PL, OL, NL, ML | R, Q, P, O, N, M, L |
Let's begin by reviewing the definition of a polyhedron.
|
A polyhedron is a solid composed of all flat surfaces that enclose a single region of space. |
Therefore, it is a polyhedron. Now, let's consider two types of polyhedrons.
The solid has one base that is a hexagon and three triangular faces that meet at the common vertex, so it is a hexagonal pyramid. Let's recall the meaning of the features that we want to identify.
Now we can name its bases, faces, edges, and vertices.
| Base | Faces | Edges | Vertices |
|---|---|---|---|
| RQPONM | RQPONM, RQL, QPL, POL, ONL, NML, MRL | RQ, QP, PO, ON, NM, MR, RL, QL, PL, OL, NL, ML | R, Q, P, O, N, M, L |