edge stellation

[Whogius]

i would like to have an option to make edge stellations of an polyhedron


that would include

- extend all (or some selection of) edges (don't think stella has an option for this. please tell me i am wrong)
- place marks/ balls where at least 3 extended edges intersect.

- allow user to add pyramids where they like.
- let stella make the polyhedron nice symmetrical again.

[robertw]

i would like to have an option to make edge stellations of an polyhedron

that would include

- extend all (or some selection of) edges (don't think stella has an option for this. please tell me i am wrong)

Maybe someday. Edge stellations should presumably include all polyhedra with edges in the same lines, even if their faces are in different planes. But for the subset with faces in the same planes you could use the existing stellation function in Stella to create such models. True edge stellation feels like a combination of stellation and faceting.

- allow user to add pyramids where they like.
- let stella make the polyhedron nice symmetrical again.

Can't you use augmentation to add pyramids on any faces? Not sure what you mean about making it symmetrical again. Might need an example.

[Whogius]

when playing with vZome ( a polyhedron app based on zometool https://www.vzome.com , online https://www.vzome.com/app/ )

you have tools like construct line- line intersection that constructs an vertex where the lines intersect.

In stella that would be like creating a vertex

also you have tools like

tools -> icosahedral symmetry that makes it all nice symmetrical again

In my hearts of hearts I would like to have a combination of vZome and Stella , stella has more options but with vzome you can start from scratch and build your own polyhedron.

(not even sure if stella can read vZome stel files.

[robertw]

Ah, so if you're using Zome, or vZome, then you don't really care about faces, only edges. In that case it seems you can already create what you want using the Stellation View. Stellations in this case would be a superset of edge stellations (actually not sure this is true). You just need to select the right stellation cells. Stella will keep the symmetry automatically.

I'm not sure you really want edge stellations anyway. If you use two edges to define a new vertex, the way you connect them together needn't be restricted to edges along the original lines.

The stellation diagram, which can be attached to a face, shows lines where that facial plane intersects with other facial planes. Points where lines meet are intersections of three facial planes, and some of those are points where two or more edges meet. All the edge-intersection points are there.

[Whogius]

Edge stellation differs from face stellation that edge stellation doesn't create new edges (it can only lengthen them) but can create new faces (also faces not on the boundary planes)

Face stellation works the other way around, face stellation doesn't create faces outside the boundary plane but can create new edges.

Maybe i can trick stella into it by first making a frame model and then adding faces to it. (not sure can stella make store faceless models?)

[robertw]

Yes understood, and no Stella doesn't have direct support for that, but the edges of edge stellations would be subsets of the stellation diagram, so you'd still be able to make edge stellations whose faces lie in the same planes as the base polyhedron. And you could use faceting mode to make ones whose faces lie in different planes.

I'd like to see some examples though, as it seems restrictive compared to face stellations or facetings. The icosahedron for example seems to only have edge stellations whose edges are the same as the original icosahedron? Maybe only the great dodecahedron if retaining full symmetry?

[Whogius]

Sorry cannot give examples , edge stellation is fundamentally different from face stellation / greatening.
The vertices in edge stellations of a polyhedron are a subset of the vertices in face stellations of the same polyhedron so i agree that there are likely less edge stellations than face stellations.
Butbthe faces are completely different

One of the nice things i presume is that edge stellations always give star polyhedra (spikey polyhedra) and i do also think beginners in polyhedra think that stelation means edge stellation . (That is how kepler started it)

But i guess it is difficult to implement, so just a suggestions.
(Also found a whole set of other actions Stella doesn't seem to support, Conway polyhedra, will make a new suggestion for that, or maybe i am wrong and just haven't found the option yet)

[robertw]

You could use the stellation diagram in combination with faceting mode to make any edge stellation, but would be up to you to make sure the result is indeed an edge stellation.

Beginners in polyhedra usually think stellation means augmentation, ie just adding spikes to faces.

Edge stellation would not always lead to spiky things. The great dodecahedron would be an edge stellation of the icosahedron. It has the same edges.

It doesn't appear that Kepler used the term stellation to mean edge stellation. The wikipedia page on Stellation has a section titled Kepler's Definition. It says:

In 1619 Kepler defined stellation for polygons and polyhedra as the process of extending edges or faces until they meet to form a new polygon or polyhedron.

He stellated the regular dodecahedron to obtain two regular star polyhedra, the small stellated dodecahedron and the great stellated dodecahedron. He also stellated the regular octahedron to obtain the stella octangula, a regular compound of two tetrahedra.

Note it says extending "edges or faces", and the great stellated dodecahedron is NOT an edge stellation of the dodecahedron. It would be an edge-stellation of the icosahedron. The stella octangular is also not an edge stellation of the octahedron.

Stella could already make any edge stellation, but it would be tricky to enumerate them, to step through them one by one.

You're right, Stella doesn't have Conway operations. I did start looking into it, but it won't be in the next release. Some day though.

[Whogius]

Beginners in polyhedra usually think stellation means augmentation, ie just adding spikes to faces.

Edge stellation would not always lead to spiky things. The great dodecahedron would be an edge stellation of the icosahedron. It has the same edges.

It doesn't appear that Kepler used the term stellation to mean edge stellation. The wikipedia page on Stellation has a section titled Kepler's Definition. It says:

In 1619 Kepler defined stellation for polygons and polyhedra as the process of extending edges or faces until they meet to form a new polygon or polyhedron.

He stellated the regular dodecahedron to obtain two regular star polyhedra, the small stellated dodecahedron and the great stellated dodecahedron. He also stellated the regular octahedron to obtain the stella octangula, a regular compound of two tetrahedra.

Note it says extending "edges or faces", and the great stellated dodecahedron is NOT an edge stellation of the dodecahedron. It would be an edge-stellation of the icosahedron. The stella octangular is also not an edge stellation of the octahedron.

Stella could already make any edge stellation, but it would be tricky to enumerate them, to step through them one by one.

You're right, Stella doesn't have Conway operations. I did start looking into it, but it won't be in the next release. Some day though.

no/yes (confused now) the great stellated dodecahedron is an edge stellation of the icosahedron (not the great dodecahedron)

but edge stellation is (sometimes) a form of just adding spikes to faces, (just in a way that doesn't create new edges).

Prisms can have multiple edge stellations (if the prism has enough sides) still not sure if other polyhedra even can have them. (just didn't manage to make one )

another thing to add to the request list - an option to select Catalan solids like you can select Archimedean solids ( just to make things easier)

[robertw]

Not sure where Catalans would fit into the library though. They're not uniform, so couldn't go near the Archimedeans, which seems wrong. And didn't want to add stuff unnecessarily when you can already get all the Catalans by loading the Archimedeans.