In this area, the architects may be ahead of us! Parametric shapes and the use of algorithms are present but still very timid! The book "From control to design" presents some example.

Designers should upgrade their skills!

Thank You Demetrio!

I think it would be helpful simply to start adding words from other languages that more effectively describe.....the english language does not use gender in its words, we could start there, additionally some words in latin based languages are simply more effective at describing concepts instead of this linear english language

I think there may be a problem in your assumptions here.  Of course unless you study contemporary architecture then what you see around you will be very limited and not representative of current thinking.  Many architects are working on new forms as you call them and many people in architectural cad play around with parametric design creating forms that can be continuously modified.  Of course Frank Gehry is well known but there are many others to.  The cube or more correctly cuboid form of the modern movement is by no means the standard today.

Hi Bryan, The classic vocabularies of Polyhedra in both the non-euclidean and euclidean versions are not known widely. The most common is the cube. The mathematics of the non-euclidean school produces a language of curved hyperbolic, standardized geometries while the CAD iterations are one of a kind no repeatable elements that can not be modular. As a result they are not created with efficiency, and economies to make them useful. I have invented a vocabulary of polyhedra based on the non euclidean mathematics of Reimann, Gauss, Bolyai and Lobachevsky the the world of design does not know about. The human mind does not like to be made aware of inventions that threaten their sense of knowing it seems. As a result we get stuck in same old paradigms. I do not make ass-u-mptions. I make inventions that defy the old views of how things work.

Herb, although I am outside of my expertise, I really enjoy the way your mind works and would like to learn more about your CAD vocabulary.

The experiment that I started with is very logical (simple). Balls of the same diameter are stacked in order. One ball is unity. it represents space contained in itself and the space around it is the world. Which of these two spaces are important to us? We generally gravitate to the space in the sphere or ball. Two spheres create duality, just more of the same. Their center form a line or an edge. When three are joined  or are touching each other they form the first two dimensional space or the interstitial space that is a non-euclidean shape. An imploded triangle. To most folks that is literally no-thing. To me that is where the fun begins. While most are engaged with the centers of the spheres forming the triangle or the Euclidean space.

The real three dimensional space and the experience of it comes when the fourth sphere is stacked onto the three on the first level. Observe the interstitial space between the walls of four spheres. Scale them up to be the size of planets or galaxies and think about how to extract the elements from the spaces with the geometry needed. This leads to an entire world of new Non-Euclidean forms. You do not need CAD for this; its intuitive, it's logic. To make it more fun use spheres of different diameters. Fuse them together as it they are made of anti matter. See them all fused back into the universal one as the source of their arising.

Now go into the world and look for these forms in nature and in our man-made environments. If you find any please let me know.

Herb, although I am outside of my expertise, Richard-NO ONE IS EVER OUTSIDE OF ANY WHERE or ANYTHING.

I really enjoy the way your mind works- THE MIND IS A USELESS THOUGHT MILL AND CAUSES US TO OVERTHINK. IT'S AN OBJECTIVE TIME TRAP and would like to learn more about your CAD vocabulary. BE OPEN IN THE ABUNDANCE OF LIFE.