Pyra Sphere - Iconic Pyra Sphere

Vertxes not 100% accurate at present

On setting up the above Geometry, I noticed that the "Pyra Sphere Nested Pipe Connector" vertexes did not have quite the correct angles required to setup the Geometry perfectly.
However as the vertexes were quite close to the correct Geometry, this allowed the Geometry to be setup, as above.
N.B. it should be noted that that the fact that the PVC conduit used bends, probably helped with the slightly inaccurate vertexes.
This may only be an issue when the Geometry is constructed with pipes that do not bend.
Will work on this issue at a later date.

Other names for this Geometry

Tetrahedron with a Truncated Tetrahedron nested inside it.

Building a Terra Sphere - Iconic Terra Sphere

You will need the following Connectors

• 4 - Pyra Sphere Pipe Connectors
• 12 - Pyra Sphere Nested Pipe Connector

You will need the following pipes

• 24 lengths (labelled "a" in image below)
• 6 lengths (labelled "b" in image below)

Length b can be any length that you want, it just depends on what kind of Geometry you wish to create.

N.B. when determining the lengths of the pipe, you will probably need to take into account that part of the connectors actually add to the length of the sides. So may need to determine what length the connectors add to your pipe lengths for the various sides and deduct this from the lengths of the pipe you produce.

Template dimensions for this Geometry

The Template use an equal lateral hexagon inside each triangular face of the Pyra Sphere - Iconic Pyra Sphere  (when used in The Template ceremonies).

To achieve this length b should be the same as length a in the above diagram.

N.B. again you will have to take into account the length the connectors add to the overall length of the sections of the Geometry i.e. have to deduct lengths connectors add to dimensions of the pipe lengths required.

Useful Maths

For a given height of Tetrahedron, the length of the side of the outer Tetrahedron is found using the formula :-

Outer Tetrahedron Side = (3 * height) / (square root of 6)

Dividing the Outer Tetrahedron Side by 3, gives the length a in the above diagram.

Files use with 3D editing packages and 3D printers

Pyra Sphere Pipe Connector

File 5 not found (getFileFromId)

File 6 not found (getFileFromId)

N.B. this is the same connector/vertex as used in the Pyra Sphere

Pyra Sphere Nested Pipe Connector

File 33 not found (getFileFromId)

File 34 not found (getFileFromId)

N.B. this vertex does not have quite the correct angles required to setup the above Geometry perfectly, although it appears to produce an acceptable Geometry using PVC Conduit (see note above).

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