does stella do primary stellations correctly?
Posted: Thu Jul 24, 2025 1:28 pm
I was puzzling with primary stellations and am wondering if stella is implementing them correctly.
as i understand primary stellations: (and i maybe wrong here)
- you would just start with an ordinary (lets call it full) stellation diagram:
The stellation diagram is a two-dimensional diagram that lies in the same plane as one of the faces of the original polyhedron, and shows a line for each intersection with one of the other face planes. The lines enclose finite areas known as elementary regions [17]. Infinite areas, i.e. those not completely enclosed by lines, are left out, and any part of a line that does not have a finite elementary region on at least one side is not shown. One stellation diagram is required for each type of face. For example, only one diagram is required for the icosahedron, as all faces share the same relationship to the whole.
for an primary stellation this would become: (in my opinion i may be wrong here)
The stellation diagram is a two-dimensional diagram that lies in the same plane as one of the faces of the original polyhedron, and shows a line for each intersection with one of the other face planes. Infinite areas, i.e. those not completely enclosed by lines, are left out, and any part of a line that does not have a finite elementary region on at least one side is not shown. One stellation diagram is required for each type of face. For example, only one diagram is required for the icosahedron, as all faces share the same relationship to the whole.
Primary lines in a stellation diagram are those that lie in a reflection plane. A primary region is an area of the stellation diagram that is enclosed on all sides by primary lines, with no other primary lines crossing the area.
so in my opinion that would result that in a primary stellation only primary regions should be considered.
a completely simpler stellation diagram would result with less (but larger) regions and (less but larger) cells.
(after more thinking as there are only 15 reflection planes there is a limit to the number of possible stellations of any polyhedron)
But that is not what Stella does. Stella does keep the full stellation and the full cell set
and that seems to work fine but if you look close at the stellation diagram you see that stella add the outside (red) faces correctly but the inner (green) faces dont keep to the primary regions.
Also selecting primary regions doesnt work per primary region, you need to select every elementary region individually.
as i understand primary stellations: (and i maybe wrong here)
- you would just start with an ordinary (lets call it full) stellation diagram:
The stellation diagram is a two-dimensional diagram that lies in the same plane as one of the faces of the original polyhedron, and shows a line for each intersection with one of the other face planes. The lines enclose finite areas known as elementary regions [17]. Infinite areas, i.e. those not completely enclosed by lines, are left out, and any part of a line that does not have a finite elementary region on at least one side is not shown. One stellation diagram is required for each type of face. For example, only one diagram is required for the icosahedron, as all faces share the same relationship to the whole.
for an primary stellation this would become: (in my opinion i may be wrong here)
The stellation diagram is a two-dimensional diagram that lies in the same plane as one of the faces of the original polyhedron, and shows a line for each intersection with one of the other face planes. Infinite areas, i.e. those not completely enclosed by lines, are left out, and any part of a line that does not have a finite elementary region on at least one side is not shown. One stellation diagram is required for each type of face. For example, only one diagram is required for the icosahedron, as all faces share the same relationship to the whole.
Primary lines in a stellation diagram are those that lie in a reflection plane. A primary region is an area of the stellation diagram that is enclosed on all sides by primary lines, with no other primary lines crossing the area.
so in my opinion that would result that in a primary stellation only primary regions should be considered.
a completely simpler stellation diagram would result with less (but larger) regions and (less but larger) cells.
(after more thinking as there are only 15 reflection planes there is a limit to the number of possible stellations of any polyhedron)
But that is not what Stella does. Stella does keep the full stellation and the full cell set
and that seems to work fine but if you look close at the stellation diagram you see that stella add the outside (red) faces correctly but the inner (green) faces dont keep to the primary regions.
Also selecting primary regions doesnt work per primary region, you need to select every elementary region individually.