Steven Dutch, Professor Emeritus, Natural and Applied Sciences, University of Wisconsin - Green Bay

Any group of crystal faces related by the same symmetry is called a *form*. There are 47 or 48 crystal forms depending on the classification used.

Closed forms are those groups of faces all related by symmetry that completely enclose a volume of space. It is possible for a crystal to have faces entirely of one closed form. Open forms are those groups of faces all related by symmetry that do not completely enclose a volume of space. A crystal with open form faces requires additional faces as well. There are 17 or 18 open forms and 30 closed forms.

**Pedion**- A single face unrelated to any other by symmetry. Open
**Pinacoid**- A pair of parallel faces related by mirror plane or twofold symmetry axis. Open
**Dihedron**- A pair of intersecting faces related by mirror plane or twofold symmetry axis. Some crystallographers distinguish between
**domes**(pairs of intersecting faces related by mirror plane) and**sphenoids**(pairs of intersecting faces related by twofold symmetry axis). All are open forms **Pyramid**- A set of faces related by symmetry and meeting at a common point. Open form.

**Prism**- A collection of faces all parallel to a symmetry axis. All are open.

- Pyramid
- A group of faces intersecting at a symmetry axis. All are open. The base of the pyramid would be a pedion.

**Dipyramid**- Two pyramids joined base to base along a mirror plane. All are closed, as are all following forms.

**Disphenoid**- A solid with four congruent triangle faces, like a distorted tetrahedron. Midpoints of edges are twofold symmetry axes. In the tetragonal disphenoid the faces are isoceles triangles and a fourfold inversion axis joins the midpoints of the bases of the isoceles triangles.
**Scalenohedron**- A solid made up of scalene triangle faces (all sides unequal)
**Trapezohedron**- A solid made of trapezia (irregular quadrilaterals)
**Rhombohedron**- A solid with six congruent parallelogram faces. Can be considered a cube distorted along one of its diagonal three-fold symmetry axes.

**Tetartoid**- The general form for symmetry class 233. 12 congruent irregular pentagonal faces. The name comes from a Greek root for one-fourth because only a quarter of the 48 faces for full isometric symmetry are present.
**Gyroid**- The general form for symmetry class 432. 24 congruent irregular pentagonal faces.
**Diploid**- The general form for symmetry class 2/m3*. 24 congruent irregular quadrilateral faces. The name comes from a Latin root for half, because half of the 48 faces for full isometric symmetry are present.
**Pyritohedron**- Special form (hk0) of symmetry class 2/m3*. Faces are each perpendicular to a mirror plane, reducing the number of faces to 12 pentagonal faces. Although this superficially looks like the Platonic solid with 12 regular pentagon faces, these faces are not regular.

**Tetrahedron**- Four equilateral triangle faces (111)
**Trapezohedral Tristetrahedron**- 12 kite-shaped faces (hll)
**Trigonal Tristetrahedron**- 12 isoceles triangle faces (hhl). Like an tetrahedron with a low triangular pyramid built on each face.
**Hextetrahedron**- 24 triangular faces (hkl) The general form.

**Cube**- Six square faces (100).
**Octahedron**- Eight equilateral triangle faces (111)
**Rhombic Dodecahedron**- 12 rhombic faces (110)
**Trapezohedral Trisoctahedron**- 24 kite-shaped faces (hhl). Note that the Miller indices for the two trisoctahedra are the opposite of those for the tristetrahedra.
**Trigonal Trisoctahedron**- 24 isoceles triangle faces (hll). Like an octahedron with a low triangular pyramid built on each face.
**Tetrahexahedron**- 24 isoceles triangle faces (h0l). Like an cube with a low pyramid built on each face.
**Hexoctahedron**- 48 triangular faces (hkl) The general form

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*Created 15 Sep 1997, Last Update
31 May 2020 *