Examples of pentadecahedraDual elongated triangular cupolaElongated pentagonal bipyramidTridecagonal prismElongated heptagonal pyramid
A pentadecahedron (or pentakaidecahedron) is a polyhedron with 15 faces. No pentadecahedron is regular; hence, the name is ambiguous. There are numerous topologically distinct forms of a pentadecahedron, for example the tetradecagonal pyramid, and tridecagonal prism. In the pentadecahedron, none of the shapes are regular polyhedra. In other words, a regular pentadecahedron does not exist, and the pentadecahedron cannot fill space; a space-filling pentadecahedron does not exist.
In chemistry, some clusters of atoms are in the form of pentadecahedra. Calculations have shown that there is a unit cell of the pentadecahedron that is stable in the crystal.
Convex There are 23,833,988,129 topologically distinct convex pentadecahedra, excluding mirror images, having at least 10 vertices.Counting polyhedra (Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.)
Common pentadecahedra NameTypeImageSymbolVerticesSidesFacesχFace typeSymmetryTridecagonal prismprismt{2,13}{13}x{}26391522 tridecagons13 rectanglesD13h, [13,2], (*13 2 2)Tetradecagonal pyramidpyramid15281521 tetradecagon14 trianglesC14v, , (*14 14)Elongated heptagonal pyramidpyramid15281527 triangles7 rectangles1 heptagonD7h, [7,2], (*227), order 28Heptagonal truncated conetruncated cone15281527 triangles7 kites1 heptagonD7h, [7,2], (*227), order 28Elongated pentagonal bipyramidBipyramidJohnson solid122515210 triangles5 squaresD5h, [5,2], (*225)
References
What Are Polyhedra?, with Greek Numerical Prefixes
External links Self-Dual Pentadecahedra,