You’re thinking of a geodesic parabolic dish — a structure made from straight struts arranged in a triangular (geodesic) pattern that automatically forms an accurate paraboloid when assembled.

This is a very real thing and widely used in home-built radio telescopes.

Here’s how it works:

1. A paraboloid can be approximated using straight edges

A true parabola is curved, but you can approximate it using many small straight segments.

If you arrange straight struts in a triangular grid, the surface will naturally bend into the required shape when all lengths are correct.

This is what a geodesic design does.

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When sized correctly, this triangular mesh forms a paraboloid.

2. “Automatic shaping” comes from the strut lengths

Each strut has a predetermined length.
Once you assemble them:

• the outer ring defines the dish diameter
• the inner rings define the depth
• the web forms the curved surface

Because all the struts force the geometry, the whole thing naturally collapses into a parabola.

There is no bending, moulding, or shaping needed.

This is why these are often called pre-stressed geodesic reflectors.

3. Known designs

Several designs exist:

(A) The Cantenna/GEODISH design

Uses concentric rings of triangles.
Plans exist online for 1–3 m reflectors.

(B) “Hobbs Geodesic Parabola”

Old ham-radio design where the dish shape is determined by cutting struts to exact lengths.

(C) “Paraclipse” commercial dishes

Large commercial reflectors using geodesic triangulation to maintain the parabola shape.

(D) “Tensegrity parabolic dish”

Uses tensioned wires + struts to pull the mesh into a paraboloid.

4. Why this works

A paraboloid satisfies:

z = \frac{r^2}{4f}

Instead of shaping a continuous surface, builders compute the 3D coordinates of each node.
Between nodes they place straight members.

Do this across the whole surface and the mesh becomes a discrete paraboloid.

5. Advantages

• Very lightweight
• Very stiff
• Uses cheap straight tubing (aluminium, PVC, wood, steel)
• Automatically forms the correct shape
• Can be scaled easily
• No large bending jigs or moulds

This is why many amateur radio astronomers build 3–5 m dishes this way.