The pentahedron [1] , or pentahedron [1] , is a polyhedron with five faces.
There are 2 topological types of pentahedra:
- a quadrangular pyramid (a pyramid can also be non-convex if its base is a non-convex quadrangle);
- a triangular prism and various polyhedrons that can be obtained by deformation of a triangular prism (this type also includes a wedge and a triangular truncated pyramid ).
The second type can also be described as the space cut out from a trihedral cylinder or trihedral corner by two planes that intersect all three faces of this cylinder or corner, but themselves intersect outside this cylinder or corner or are parallel.
There is no pentahedron in which all faces are the same.
| Title | Picture | Top | Riber | Facets | Face type |
|---|---|---|---|---|---|
| Quadrangular pyramid |  | 5 | 8 | 5 | 4 triangles 1 rectangle |
| Triangular prism |  | 6 | 9 | 5 | 2 triangles 3 quadrangles |
Regular polygons
There are two pentahedra in which each face is a regular polygon :
- a square pyramid , the side faces of which are regular triangles;
- regular triangular prism, the side faces of which are squares.
If we denote the length of the face of such a pentahedron a , then its volume will be
-
(for the pyramid)
-
(for prism)
and surface area
-
(for the pyramid)
- (for prism)
Notes
- β 1 2 English-Russian Dictionary of Mathematical Terms / Ed. P.S. Aleksandrova. - 2nd, corrected and add. ed .. - M .: Mir, 1994 .-- S. 200. - 416 p. - ISBN 5-03-002952-4 .
Links
- Weisstein, Eric W. Pentahedron on Wolfram MathWorld .