**Icosahedron Surface** creates a surface representing
a linear interpolation between an icosahedron and a sphere.
The surface is for comparison to virus particles with icosahedral symmetry;
it can be colored by density data for such structures with
**Surface
Color**. **Icosahedron Surface** information is saved in
sessions.
See also:
**shape
icosahedron**,
**hkcage**,
**meshmol**,
**Cage Builder**

There are several ways to start
**Icosahedron Surface**, a tool in the
**Higher-Order Structure** category.

Clicking **Show** creates the surface according to the settings:

**Radius**- radius of the sphere component and distance from the center to a vertex of the icosahedron component (the default is**100**display units, generally Å); the value can be changed by entering a different number or by moving the slider.**Sphere factor**- weight to use for the sphere component, where**0**(default) yields an icosahedron and 1 yields a sphere; the value can be changed by entering a different number or by moving the slider. Values outside the range 0-1 can be used, but negative values such that surface points pass through the origin will cause subsequent**Sphere factor**settings to produce the wrong surface.**Orientation**- orientation of the icosahedron**xyz 2-fold axes (222)**(default) - with two-fold symmetry axes of the icosahedron along the x, y and z axes. In the untransformed icosahedron, apoints at the user. (Objects are untransformed when no rotations/translations have been performed, or when the view has been*vertically oriented edge***reset**to the default.)**xyz 2-fold axes, alt (222r)**- as above, except rotated 90° about the z axis. In the untransformed icosahedron, apoints at the user.*horizontally oriented edge***x 2-fold, z 3-fold (2n3)**- with a two-fold symmetry axis of the icosahedron along the x axis and a three-fold symmetry axis along the z axis. The y axis does not coincide with a symmetry axis. Aof the untransformed icosahedron points at the user.*face***x 2-fold, z 3-fold, alt (2n3r)**- as above, except rotated 180° about the y axis.**x 2-fold, z 5-fold (2n5)**- with a two-fold symmetry axis of the icosahedron along the x axis and a five-fold symmetry axis along the z axis. The y axis does not coincide with a symmetry axis. Aof the untransformed icosahedron points at the user.*vertex***x 2-fold, z 5-fold, alt (2n5r)**- as above, except rotated 180° about the y axis.**y 2-fold, z 5-fold (n25)**- with a two-fold symmetry axis of the icosahedron along the y axis and a five-fold symmetry axis along the z axis. The x axis does not coincide with a symmetry axis. Aof the untransformed icosahedron points at the user.*vertex***y 2-fold, z 5-fold, alt (n25r)**- as above, except rotated 180° about the x axis.

**Subdivision factor**- how finely to subdivide the surface. A factor of**1**(default) yields 20 triangles, the 20 faces of the icosahedron. Values represent the number of subdivisions within an edge of the icosahedron, and only non-negative powers of 2 are used (1, 2, 4, 8, ...). Other numbers can be entered, but will be rounded to a power of 2. The**spacing**is the length of a subdivision.**Surface style**- whether the surface should be shown as**solid**or**mesh****Color**- a color well specifying the surface color**Line width**- pixel width of lines in the**mesh**style

**Rounded edges**.
Even when the **Sphere factor**
is zero, the edges of the icosahedron may appear to be rounded
because of the way the model is lit.
This is especially noticable in the **solid**
style.
Each surface vertex has a normal vector that determines how light
reflects off the surface.
The vertices at the edges between faces of the icosahedron
have a normal vector midway between the normals of the faces.
This causes the edges to appear rounded instead of sharp.
A higher **Subdivision factor**
(*e.g.*, 32 or 64) will make the edges look sharper.

**Coloring**.
The **Surface
Color** tool assigns each surface vertex a color;
between vertices, the colors are interpolated.
More detailed color variations will be apparent with a higher
**Subdivision factor**.

UCSF Computer Graphics Laboratory / July 2014