Let me get back to the idea of using the as a logo. As I mentioned already this has been recently proposed as a “typographically available” alternative to the proposed Fediverse logo, design built around a fully connected pentagon that I've recently replicated by hand.

If your browser/font/operating system combination supports it, this is what the asterism looks like for you, enlarged to 250%:

⁂

It's not a bad choice to represent something which is a constellation of interconnected instances, and plays around on the ambiguity of asterism as both a typography and an astronomy term.

For inline text, talking about the ⁂Fediverse⁂ thus makes perfect sense, even if the actual presentation of the asterism will change from reader to reader, depending on the font of choice: do the asterisks have 5, 6 or 8 points? are the bars forming the asterisks straight or ornate? do they cross at equal angles or are some closer than others? are they staggered or layered? There's a lot of variation on how it may look, and it will be different for all (the Wikipedia page on Asterism has a few variations to show).

One thing that all these designs (or at least the ones I've seen) have in common is that the asterisks don't actually connect. Also, the large variety of presentations mean one can't actually rely on it for anything: just the general concept. So what happens if we actually try to do something about it?

The idea came to me because I noticed that with 6-point asterisks with equal angle opening, their placement on the vertices of a triangle almost showed a hidden figure. So I decided to try and make it more explicit, with this result:

Three 6-points asterisks at the vertices of an equilateral triangle. The design reveals a figure in the center that looks like the projection of a cube
A carefully designed asterism with three 6-points asterisks.

If you're like me (or my son) you'll see a classic “hidden cube” emerge from the contact of the asterisks.

This is a surprisingly effective design, and if a schematic monochrome representation of the Fediverse is desired, this would be a serious contender, possibly winning over the monochrome pentagon logo I presented previously.

I also tried to achieve a similar effect with the 5-point asterisk, but couldn't make it work without rotations:

Three 5-points asterisks at the vertices of an equilateral triangle. The bottom two are rotated so the “base” points all touch, forming a pseudo-triangular shape in the middle.
A carefully designed asterism with three 5-points asterisks.

I find this interesting as well, although I think that rather than this in itself, it could be an inspiration for a different idea, such as a gem-like design obtained intersecting three arcs at τ/3 (that's 120°).

I couldn't stop there, so I thought, what if instead of three asterisks we use five 5-point asterisks, or even better six (one in the middle)? There's actually some interesting designs that can come of such an idea, four of which can easily be obtained with simple π=τ2 rotations of either the central or lateral asterisks:

A spoked gear A spoked wheel
A snowflake A papercraft
The four asterisms that can be obtained from six 5-point asterisks (a central and five lateral ones) rotating the central and lateral one alternative by 0° and 180°.

All of these are interesting designs, in my opinion. An objection that could be raised against them is that the central asterisks may give an idea of “centralization” that is antithetic to the spirit of the Fediverse, but if we consider the “central” star not a specific instance but “the instance the user is on”, the “spoked cartwheel” and “snowflake” designs are actually surprisingly good at representing how messages travel in the Fediverse, from the user to its connections, and then out towards the rest, from connection to connection.

May be worth looking into.