How do I modify a solid?

[tpgettys]

Can you tell me if/how to create an image of an icosahedron with one vertex truncated?

I would most appreciate a step-by-step explanation; in the past I have received instructions that assumed I knew much more than I do about how to use Stella, and so was discouraged from following up.

[Dinogeorge]

In this case, first call up a truncated icosahedron. Then set its symmetry to "No symmetry." Then stellate it using the stellation diagram (which is very wide because there's no symmetry and the stellachunks are handled one at a time). Twelve of the rectangles in the second row of the diagram correspond to stellachunks that lie on top of the pentagonal faces. You have to find them by selecting each rectangle in turn (ctrl+left click) until your "stellation" needs only one more such stellachunk to become the complete icosahedron. Undo any stellachunks that you don't want by selecting their rectangles a second time. Finally, put the model into memory and retrieve it as a fresh model. It's clumsy, but it works (just did it myself as a test).

[Dinogeorge]

It occurred to me that you can do it faster by selecting the symmetry as "5-fold pyramidal." This gives you most of the stellachunks you want to add to the truncated icosahedron in two groups of five at a time. The stellation diagram is correspondingly smaller, too.

I assume you want the single stump face to be the "right size," that is, the size it would be if it were truncated the Archimedean way.

[robertw]

...Then stellate it using the stellation diagram (which is very wide because there's no symmetry and the stellachunks are handled one at a time). Twelve of the rectangles in the second row of the diagram correspond to stellachunks that lie on top of the pentagonal faces.

You are referring to the cell diagram here (a tree of rectangles). The stellation diagram lies in a facial plane showing all lines of intersections with other face planes.

Finally, put the model into memory and retrieve it as a fresh model. It's clumsy, but it works

Less clumsy: click on the left-and-down arrow button in the title bar of the stellation view. Most views have one of these. It uses whatever's in that view as the new base model.

Tom, George is right, although I don't often use the cell diagram, as it's trial and error to figure out what each cell refers to. Follow these steps:

• Start with the truncated icosahedron (Ctrl+N, ti, Enter)
• I suggest the base polyhedron view on the left, and the stellation view on the right.
• Optionally: Untick Options->Recolor Sub-Symmetries (so colours don't change in the following step)
• Choose "5-fold Pyramidal" from the subsymmetry drop-down list (initially showing "Icosahedral").
• Display the symmetries so you can see which 5-fold axis was kept (Display->Show Symmetry Axes or just hit "s").
• There are several ways to select the stellation cells you need. The following is how I'd do it. Select Selection->Selected Face Display->Show Stellation Diagram (there's also a toolbar button for this).
• Select a hexagon (Shift+Left-click on it). Instead of a highlighted face you'll see the whole stellation diagram in the plane of the face.
• Select the stellation cells you need, again with Shift+Left-click. See image below. Repeat with other hexagonal faces as necessary.
• Click the left-and-down arrow button at the top of the stellation view.

[Ulrich]

More easily, you can use faceting technique in this case: change the symmetry to 5fold pyramidal, then subdivide the faces by 3 and facet out the top pentagon, the lateral tetragons and the unchanged triangles, that's all.

Ulrich

[robertw]

Good idea Ulrich. Here's a pic in case anyone can't follow this:



Use "Poly->Subdivide Faces" to get the tesselation required.

You're right that this will only work in this case. For a dodecahedron with one vertex truncated, dividing the edges in 3 would not match the Archimedean truncated dodecahedron.

Here's yet another way to do it, which would work in either case. Start with the truncated icosahedron. Select a hexagon face and use "Scale->Base Polyhedron Inradius", setting the distance to 1 say. Put this in a memory slot. Then load the icosahedron, and again set the inradius to 1. Now blend the two models with "Edit->Add/Blend from Memory". Now faceting mode can again be used to create the final model we want. It's a bit easier to facet this time since Ctrl+Right-click can be used to create most of the faces with a single click, since they are still present in the original model.



Rob.

[Major Mayhem]

If the OP wanted to know how to remove a vertex from a polyhedron, then the ideas presented are good. However, if he just wanted a truncated icosahedron, then it already exists in Stella as the gyroelongated pentagonal pyramid, J11, a Johnson solid.