This research deals with generation of double curvature forms with a single module: an equilateral triangle. Keywords: dome, geodesic, engineering, invention, discovery, find out, geometry, cupola, coupole, network, strut, connector, node, hub, building, space, structure, architecture, triangle, equilateral, identical, double curvature, doubly curved surface form, Lobel, form, business, venture capital

Think of an application for Lobel Frames, other than architecture ? Let us know !
The family TRA
1/ Generalities

1.1/ The origin : A module composed of modules (again).

Here is the third family of closed forms. By this, I mean forms closed within themselves. This idea came to me when I first noticed that family C6 forms were sufficiently flexible to adopt certain proportions allowing them to surround a tetrahedron..
This family is thus the third and last of my families to establish a connection with platonic volumes. To illustrate the explanation, I used the form 60P35P3.C6, but I could have used form 60P35P2.C6 or P4 or P5, etc. (See C6 family)
This form is interesting in this particular case because its three suspension points can rest on each vertex of the triangle that make up the tetrahedron. I calculated the slope of the angle at 35.26438968275466° which is (as any geodesic-man knows..) the half angle that makes up the faces of the tetrahedron...! (Figures: Tra Module - Joining and Tra the classic sights)



The shapes are then placed on each faces of the tetrahedron. As their openings line up joining perfectly, a closed volume with three orthogonally symmetric planes is formed. I call this shape "the mother form". Each tip of this form is inscribed in a sphere.



This mother shape has twelve symmetrical planes in which only one is interesting as the others are just repetitions.
(Figure Section 1 12-4-0)



By cutting it by its principal symmetrical planes, I get one family, TRA. (Figure Tra Mother shape)

1.2/ Diversification

After having cut the mother form by its symmetrical plane, the shape lies completely on a plane.
If we consider each vertex as being articulated, the half form is not rigid in itself, but thanks to the miracle of the god of structures, we easily understand when the base line is rigid, either because it is fixed on the plane (on the ground) or by any other means of rigidifying the line, the entire form becomes completely inflexible. Of course, by this I mean geometrically rigid (which is already considerable).
The materials, being pliable, do not behave (alas, or so much the better!) like perfect straight lines in geometry.

When carefully examining Tra mother shape n°22 et n°32, one notices (see arrow) that the broken line directly under the one on the ground is not quite horizontal. As in the preceding CSM or CUB family case, I strung out this line towards the horizontal.



1.3/Architectural remarks

No special remarks except that I have not studied projects yet using these forms. I would like very much that you suggest me some examples of uses.