## Compound of 3 Rhombic Prisms

For general discussion of polyhedra, not necessarily Stella-specific.
jos smits
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Joined: Fri Oct 24, 2014 2:07 pm

### Compound of 3 Rhombic Prisms

Robert Austin excited me with his model of a compound of 3 Rhombic Prisms made with Stella. I asked him how he made it but he answered that he had no idea.... intuitive action so to say.
That excited me even more and after a lot of work I found out by plane geometry (quite interesting geometry) all the measurements needed, so I can start building.
But: I would really like to know how you can make this rubust AND elegant compound with Stella. I cannot even succeed in making ONE Right Rhombic Prism because when I try to put another Triangular Prism on the selected square face of a first Triangular Prism (Put model on face) the program places it the wrong way. Someone has an idea ? And,most important, how can I put these 3 brothers together in a harmonious way ????

Pictures model:
https://www.dropbox.com/s/c5clxm00wooer ... 9.png?dl=0
https://www.dropbox.com/s/xr2y1j4jnrazr ... s.gif?dl=0

Ulrich
Posts: 133
Joined: Tue Jan 29, 2008 8:08 am
Location: Germany
Contact:
Jos,

it can be constructed quickly in the following way:

You choose the triangular prism (hit 3,4,4 and ok in the search field). You put this into memory 1. Then you select a square face and augment it by the model in the memory 1 (selected face only, and right (->), to get the orientation ok). You have stella blend parallel faces. So you got the rhombic prism and you put it into memory 9.
You choose the cube (4,4,4) and you add the model from memory 9 (menu: edit - add/blend from memory) and put this into memory 8 after having selected a face of the cube parallel to a "sharp edge" of the rhombic prism. Then you select a cube's face parallel to a "shallow edge" of the rhombic prism and you hit "a" for augmentation, selected face only and excavate (eventually you have to hit -> again for the correct orientation). You get a compound of two rhombic prisms which you put into memory 7. You choose the cube again and add the model from memory 7. Then you select a cube's face not parallel to an acute prism's edge and excavate it in the same way as before by the model in memory 8, that's it. Its dual ist pretty too, a compound of three distorted octahedra.

Ulrich

jos smits
Posts: 15
Joined: Fri Oct 24, 2014 2:07 pm
Not that easy. Even after two hours I could nor get the result, I suppose through lack of real understanding on my part. Please see my remarks in your text.

it can be constructed quickly in the following way:

You choose the triangular prism (hit 3,4,4 and ok in the search field). You put this into memory 1. Then you select a square face and augment it by the model in the memory 1 (selected face only, and right (->), to get the orientation ok). You have stella blend parallel faces. So you got the rhombic prism and you put it into memory 9.
You choose the cube (4,4,4) and you add the model from memory 9 (menu: edit - add/blend from memory)(So far I am ok.)
and put this into memory 8 after having selected a face of the cube parallel to a "sharp edge" of the rhombic prism. "Sharp edge", I suppose you mean the four edges of the Rh. Pr. that are not edges of the 2 rombs.) Can I select a random one of these ?And what is the effect of putting a model in a memory slot with a face selected ? And why do I have to put this in memory slot 8 when I will not use the model in slot 8 later anyway ?Then you select a cube's face parallel to a "shallow edge" One of the rombs edges ok ? Any special face ? of the rhombic prism and you hit "a" for augmentation, selected face only and excavate With the Rhombic Prism from memory slot 1 ?eventually you have to hit -> again for the correct orientation) Please tell me the orientation number. You get a compound of two rhombic prisms which you put into memory 7. You choose the cube again and add the model from memory 7. Then you select a cube's face not parallel to an acute acute being what you called sharp before ok ?Any particular face? prism's edge and excavate excavate with Rh Pr from slot 1 again I suppose. Orientation number ?it in the same way as before by the model in memory 8, that's it. Its dual ist pretty too, a compound of three distorted octahedra.

Hopefully you can see my red text.

Jos

jos smits
Posts: 15
Joined: Fri Oct 24, 2014 2:07 pm
slot 1 should be slot 9. sorry ulrich !

Ulrich
Posts: 133
Joined: Tue Jan 29, 2008 8:08 am
Location: Germany
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Seems that I was a little too hasty describing the procedure. In the rh prism, there are 8 edges where squares and rhombs meet at 90° and 4 edges where only squares meet. At two of the latter ones, the squares are forming an acute angle (=> "acute edges"), at the other ones the angle is shallow (=>"shallow edges", see picture).

You can choose a random one of the two squares of the cube lying parallel to the acute edges of the rh prism (see picture). If you plan to use a model for augmentation or excavation, it is useful to select a face before putting it into the memory. The selected face will then be put on the desired face of the target polyhedron.

quote:Then you select a cube's face parallel to a "shallow edge" One of the rombs edges ok ? (see picture) Any special face ? (no, any one of the two) of the rhombic prism and you hit "a" for augmentation, selected face only and excavate With the Rhombic Prism from memory slot 9 ? No with the model in memory 8 (I forgot to mention that).

quote: eventually you have to hit -> again for the correct orientation Please tell me the orientation number. In my program it is orientation 1 of 2.

quote: Then you select a cube's face not parallel to an acute acute being what you called sharp before ok ? Yes, sorry! Any particular face? any of the two posible ones.
quote: ...and excavate excavate with Rh Pr from slot 9 again I suppose. No, you take the model in memory 8. Orientation number ? orientation 1 of 2.

There might be some difficulty in the second step, the addition of the rhombic prism to the cube. Stella is behaving somehow arbitrarily: On one of my machines, this works very easily: the 2fold axes of the prism are coinciding with the 4fold ones of the cube. On another machine, this isn't the case, the prism is somehow rotated in the cube, so I had to take some detours to get it in the correct orientation.
Ulrich

jos smits
Posts: 15
Joined: Fri Oct 24, 2014 2:07 pm
hallo ulrich,

many thanks for your second message with magnificent images. I had understood your acute/shallow (obtuse is another word for this)explanations right from the beginning it seems (although in a strict geometrical sense the 2 acute edges AND the 2 obtuse edges are parallel to all 4 square faces methinks . javascript:emoticon(':shock:'))
But... my problem seems to be the position of the added Rh. Pr. in the cube- as you mentioned already.
I work on 2 pc's and both show the Rh.Pr. rotated somehow in the cube. See picture.
Too bad for me.Now the game becomes very complicated.
I would appreciate very much if you could send me the .stel files of Rh.Pr. in Cube, so I can try to continue from there and the .stel file of the compound of 3 Rh.Pr. so I can at least and at last check the measurements of the model I already built.
Picture : https://www.dropbox.com/s/0rxfbj63cn1jj ... 7.png?dl=0

jos.smits1@gmail.com Vielen Dank fuer Alles !!!![/img]

Ulrich
Posts: 133
Joined: Tue Jan 29, 2008 8:08 am
Location: Germany
Contact:
jos smits wrote: But... my problem seems to be the position of the added Rh. Pr. in the cube- as you mentioned already.
I work on 2 pc's and both show the Rh.Pr. rotated somehow in the cube. See picture.

https://www.dropbox.com/s/0rxfbj63cn1jj ... 7.png?dl=0

Too bad for me. Now the game becomes very complicated.

This is not that complicated:

You take the rhombic prism, subdivide the faces by 2 and put this into a memory slot. Then you facet a cuboid and two kinds of triangular prisms (see
picture:

You will need the model in the memory for that. Don't forget to save all the results in files or memory slots).
Then you add the cuboid to a cube (It will be orientated correctly):

You augment the "lateral" faces of the cuboid with the prisms, you created before (see picture):

and have stella blend coplanar faces. That's it.

Ulrich

robertw
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jos smits wrote:my problem seems to be the position of the added Rh. Pr. in the cube- as you mentioned already
Picture : https://www.dropbox.com/s/0rxfbj63cn1jj ... 7.png?dl=0[/img]
I had the orientation problem too when I first tried, but it worked the second. I know why though. It depends which square of the triangular prism you augment, despite them all being symmetrically the same!

Start with the triangular prism. Use "View->Orientation->Default Orientation". You'll notice that one square face is facing to the right, while the other two are facing diagonally left and forward/backward. You need to augment the square facing right. That way the default orientation of the resulting rhombic prism will match that of the cube when you add them together.

Pretty magic and cryptic I know! Ideally someday I should make the add-from-memory a bit more clever about orientations!

Ulrich
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Joined: Tue Jan 29, 2008 8:08 am
Location: Germany
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robertw wrote:
Pretty magic and cryptic I know! Ideally someday I should make the add-from-memory a bit more clever about orientations!
And doing that, could you please take care of the "put models on faces"-tool too?

Ulrich

jos smits
Posts: 15
Joined: Fri Oct 24, 2014 2:07 pm
Many thanks for all the great help Ulrich, Robert. Especially the wonderful images make understanding easier. But I still need a little time because all this is`cryptic and magic`indeed.

jos smits
Posts: 15
Joined: Fri Oct 24, 2014 2:07 pm
And now, in the middle of the night, the magic is complete. I got it !

jos smits
Posts: 15
Joined: Fri Oct 24, 2014 2:07 pm
Arcor seems dead. Probably suicide... Not a nice thing to discover after you spent an hour to write a friendly reply with some pictures.

jos smits
Posts: 15
Joined: Fri Oct 24, 2014 2:07 pm
Model finally made with top angle of 36 degrees.

See: https://www.dropbox.com/s/jqizixvtdjajp ... 6.JPG?dl=0

Many thanks.
Jos.