A hexadecahedron (or hexakaidecahedron) is a
polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.
A convex polyhedron is the convex hull of finitely many points, not all on ...
with 16
faces
The face is the front of an animal's head that features the eyes, nose and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities may affe ...
. No hexadecahedron is
regular; hence, the name is ambiguous. There are numerous topologically distinct forms of a hexadecahedron, for example the
pentadecagonal pyramid,
tetradecagonal prism
In geometry, a prism is a polyhedron comprising an polygon base, a second base which is a translated copy (rigidly moved without rotation) of the first, and other faces, necessarily all parallelograms, joining corresponding sides of the two ...
and
heptagonal antiprism
In geometry, the heptagonal antiprism is the fifth in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.
Antiprisms are similar to prisms except the bases are twisted relative to each ot ...
.
Convex hexadecahedra
There are 387,591,510,244 topologically distinct ''convex'' hexadecahedra, excluding mirror images, having at least 10 vertices. (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.)
Self-dual hexadecahedra
There are 302,404 self-dual hexadecahedron, 1476 with at least order 2 symmetry.
Symmetries of Canonical Self-Dual Polyhedra
/ref> The high symmetry self-dual has chiral tetrahedral symmetry
150px, A regular tetrahedron, an example of a solid with full tetrahedral symmetry
A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection ...
, and can be seen topologically by removing 4 of 20 vertices of a regular dodecahedron
In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagon ...
and is called a tetrahedrally diminished dodecahedron
In geometry, a tetrahedrally diminished dodecahedron (also tetrahedrally stellated icosahedron or propello tetrahedron) is a topologically self-dual polyhedron made of 16 vertices, 30 edges, and 16 faces (4 equilateral triangles and 12 identical ...
.
Examples
The following list gives examples of hexadecahedra.
* Heptagonal antiprism
In geometry, the heptagonal antiprism is the fifth in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.
Antiprisms are similar to prisms except the bases are twisted relative to each ot ...
* Gyroelongated pentagonal pyramid
In geometry, the gyroelongated pentagonal pyramid is one of the Johnson solids (). As its name suggests, it is formed by taking a pentagonal pyramid and "gyroelongating" it, which in this case involves joining a pentagonal antiprism to its base ...
* Gyroelongated square bipyramid
In geometry, the gyroelongated square bipyramid, heccaidecadeltahedron, or tetrakis square antiprism is one of the Johnson solids (). As the name suggests, it can be constructed by gyroelongating an octahedron (square bipyramid) by inserting a s ...
* Augmented dodecahedron
In geometry, the augmented dodecahedron is one of the Johnson solids (), consisting of a dodecahedron with a pentagonal pyramid () attached to one of the faces. When two or three such pyramids are attached, the result may be a parabiaugmented d ...
* Truncated triakis tetrahedron
References
What Are Polyhedra?
with Greek Numerical Prefixes
External links
Polyhedra
{{polyhedron-stub