isometric forms

isometric forms

[¦ī·sə′me·trik ′fȯrmz]
(mathematics)
Two bilinear forms ƒ and g on vector spaces E and F for which there exists a linear isomorphism of E onto F such that ƒ(x,y)= gx, σ y) for all x and y in E.
References in periodicals archive ?
There is also--and this is part of what I meant earlier by "playful"--a piece by Erich Offermann and Pete Richards called "Fluorite Balls From Hell," in which a computer-enabled, almost insanely detailed crystallographic analysis is offered of tiny fluorite crystals from Germany which typically look like spheres because they combine the hexoctahedron (48 faces), tetrahexahedron (24 faces), cube, dodecahedron, trapezohedron and (for all I could tell, on a quick read) even more isometric forms, all in more or less equal development.
In some cases (for example, "A Mighty Fortress Is Our God" or "Wake, Awake, For Night Is Flying"), the melodies appear in both rhythmic and isometric forms.
ISOMETRIC FORMS OTHER THAN THE DODECAHEDRON WHICH MIGHT FORM ELONGATED TWINS
This can be done for the various isometric forms by the following sequence of operations: (a) choose a Ft [l11] twinning axis on a crystal model or drawing; (b) identify faces which may make up a belly band on twinning; (c) show that the Miller Indicesa of a chosen face apparently parallel to the twin axis do indeed satisfy the zonal equation as before; and (d) show that an adjacent face with a similar orientation is 60[degrees] from the first face.
The terminal faces of the isometric forms referred to a pseudo-hexagonal axis system are various positive and negative rhombohedra and scalenohedra.