"Gyroid" redirects here. For the creature, see Animal Crossing (video game).

A gyroid is a certain infinitely connected triply periodic

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

 minimal surface

Minimal surface

In mathematics, a minimal surface is a surface with a mean curvature of zero.These include, but are not limited to, surfaces of minimum area subject to various constraints....

 discovered by Alan Schoen in 1970.

The gyroid has space group

Space group

In mathematics and geometry, a space group is a symmetry group, usually for three dimensions, that divides space into discrete repeatable domains.In three dimensions, there are 219 unique types, or counted as 230 if chiral copies are considered distinct...

 Iad. Channels run through the gyroid labyrinths in the (100) and (111) directions; passages emerge at 70.5 degree angles to any given channel as it is traversed, the direction at which they do so gyrating down the channel, giving rise to the name "gyroid".

In 1986, Osserman proved that it contains no straight lines, in 1996 Große-Brauckmann and Wohlgemuth

Wohlgemuth

Wohlgemut is a German surname.The word wohlgemut means 'in high spirits'. The first part of this compound is an adverb meaning 'good' , the second part is an adjective meaning 'in mood' or 'moody'...

 proved that it is embedded

Embedding

In mathematics, an embedding is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup....

, in 1997 Große-Brauckmann proved that it has no reflectional symmetries

Reflection symmetry

Reflection symmetry, reflectional symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry.In 2D there is a line of symmetry, in 3D a...

.

A gyroid surface can be trigonometrically approximated by the equation:

Other

In nature, gyroid structures are found in certain block copolymers. In the polymer phase diagram, the gyroid phase is between the lamellar and cylindrical phases.

External links

• Rotatable picture of a gyroid's period