NEXOGON: More tips using part 27255

Let's take another breather from the amazing builds using LEGO® NEXO KNIGHTS™ Combo NEXO Power shields and explore the geometry of this new piece further, this time with regular contributor Gary Davis (Bricks for Brains). 

The Nexogon joins a small family of LEGO® elements with attachment points at a rotation separation of 60° (and 30° in some cases).

Joining Nexogons at the bar

To explore some 3D geometry using the Nexogon, I wanted to join them together as close as possible along their longest side.

I settled on using two 1x2 modified plates with vertical clips (Design ID 11476) joined with an intermediate 1x2 plate. It also works with 1x1 clips and plates of course, but the 1x2 arrangement prevents any undesired misalignment.

The resulting gap is about 1 mm which just is enough to allow the Nexogons to be hinged with respect to the clip assembly and with respect to each other.

When hinged to the fullest extent possible, the Nexogon on the stud side of the block can hinge to about 48°, whilst that on the anti-stud side is limited to about 28°.

3D shapes

The hinge arrangement I've chosen doesn't allow the formation of a tetrahedron (a triangle-based pyramid), but does allow a square-based pyramid. (It's a truncated square-based pyramid of course because the Nexogons are not complete equilateral triangles).

A pair of these assemblies can then be combined to form a truncated octrahedron, shown below left.

It's also possible to cluster together two or more octrahedrons, shown below right.

Joining five Nexogons forms a truncated pentagon-based pyramid. (Of course, joining six Nexogons in this way simply forms a 2D shape.)

Joining two of these together creates a shape that I couldn't find a name for, so I'll skip over that because what is far more interesting is what happens when one joins 20 Nexogons together in this way...

Behold, the truncated icosahedron!

Clustering several pentagon-based pyramids would create a much larger shape based around a dodecahedral core but it would take 60 Nexogons to complete it; there are 20 in use in the image below.

In fact, it would need some internal bracing to maintain the form.

Joining Nexogons via the studs

I've explored a few combinations by connecting the Nexogon's studs but there's nothing very exciting to report.

Alignments

The Nexogon introduces some interesting alignments, and several non-alignments.

The transparent plates show that none of the anti-studs correspond with the studs on the other areas of the Nexogon. Neither could I find any half-stud (jumper) arrangements that would correspond (see top right).

However, the spacing of the bar, centre hole and centre of the 2x2 stud arrangement, are each spaced by 2 studs.

The lower two images show how the alignments work in conjunction with a couple of the other elements in the "60° family".

[Note from Ed: It's interesting to see different approaches to the same geometric discovery as made by Gary compared to Neil Crosby, as shown last week.]

Centre connection

The centre connection of the Nexogon is designed to receive a Technic pin. But for some reason it's a very sloppy fit, as can be seen in the image below.

Just as a point of interest, the macaroni tube joins to Nexogons such that their long edge is neatly touching.

Another surprising and disappointing feature of the centre hole is the fact that it is too wide to clutch a stud.

In the image, the 1x1 round brick is simply resting in the centre hole. If this Nexogon was turned upside down, the 1x1 round brick would simply fall out. The same is true on the underside of the Nexogon.

Building with Nexogons

With all this geometry and alignments to play with, I still haven't around to seriously building with the Nexogon. But here are a couple of tablescraps.

A three sided tower/spacecraft

A tripod landing leg

This is based very loosely on those from the Nostromo in Alien. I like to imagine the footprint that this would leave on the planet surface!

READ MORE: See Neil Crosby's geometric explorations of the Nexogon

Products mentioned in this post were kindly supplied by the LEGO Group. All content represents the opinions of New Elementary authors and not the LEGO Group.

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