Terra Sphere - Iconic Terra Sphere

This above image is the second attempt at this geometry (this one had an equilateral hexagon as part of the sides, the initial attempt the hexagon that is part of the sides, did not have equal length sides, see images below).

It was noted that it sides were not exactly cube like i.e. slightly bent out of shape.

This could have been due to :-

• Ground not not being completely level
• Plastic PVC conduit bending, either due to ground not being level, or pipe not being rigid enough
• Pipe dimensions and connectors not being completely consistent

N.B. will attempt to resolve these issues in a later builds/setup of this Geometry.

Other names for this Geometry

Cube with a Truncated Cube nested inside it.

Building a Terra Sphere - Iconic Terra Sphere

You will need the following Connectors

• 8 - Terra Sphere Pipe Connectors (nested alignment)
• 16 - Terra Sphere Nested Pipe Connector - Type 1
• 8 - Terra Sphere Nested Pipe Connector - Type 2

N.B. the Type 1 and Type 2 connectors are effectively the same, apart from the orientation of the bolt holes. So you only need the different Type 1 and Type 2 connectors if you are going to bolt the Geometry together.

Also you only need the nested form of the Terra Sphere Pipe Connector, if you are going to bolt the Geometry together.

You will need the following pipes

• 24 lengths (labelled "a" in image below)
• 24 lengths (labelled "c" in image below)
• 24 lengths (labelled "d" in image below)

The sides labelled "a" and "c" in the above diagram form the standard right angled triangle as used in the Pythagoras theorem (square of the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides).

So side c = square root of ( a² +  a² )

Side d 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.

The following image shows an example of a Terra Sphere - Iconic Terra Sphere with sides that contain a hexagon with unequal sides.
N.B. see comments at top of page on sides not being exactly straight.

Template dimensions for this Geometry

The Template use an equal lateral octagon inside each square face of the cube of the Terra sphere - Iconic Terra Sphere  (when used in The Template ceremonies).

Length "a" can be calculated with either a = S / 2.414 or a = S x 0.41421.

Length "e" can be calculated with either e = a / Square root of 2 or e = (S - a) / 2

N.B. if using this form of calculation then taking into account the length the connectors add to the overall dimensions is probably more important i.e. have to deduct lengths connectors add to dimensions from pipe lengths required.

N.B. the Wikipedia article on Octagon's contains useful information on the construction Octagon's which relate to the construction of this Geometry.

The following image shows an example of a Terra Sphere - Iconic Terra Sphere with sides that contain an equilateral hexagon.
N.B. see comments at top of page on sides not being exactly straight.

Files use with 3D editing packages and 3D printers

Terra Sphere pipe Connector - nested alignment

N.B. The the above Terra Sphere corner pipe connector is not the same as the Terra Sphere pipe Connector. It has been adjusted so the bolt holes allow pipes with aligned bolt holes to be easily connected.

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Terra Sphere Nested Pipe Connector - Type 1

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Terra Sphere Nested Pipe Connector - Type 2

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N.B. the difference between Type 1 and Type 2 Terra Sphere Nested Pipe Connector is how the bolt holes are aligned. This should allow pipes with aligned bolt holes to be connected to the Vertexes.

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