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I want to snap the center of the circular plane to the vertex of the tetrahedron while rotating the cone around the origin (keeping its' peak in the origin).

I have made a vertex at the center of the circular base, but it's not showing up in object mode, and does not appear to be interactive in a snapping manner.

I realize this could also be done just by knowing the angle (and, in this case, rotating along the X axis), but I'm not aware of an embedded way to determine it.

Generally, in dealing with symmetrical manipulations, it would be nice to have a snapping grid that conforms to certain form. The regular cartesian could then be called "octahedral" since there are 3 axes x,y,z , and the next in axis count would be "tetrahedral"(one I would be using in this example) which would have all the common options that constrict manipulation to given axes. Just a suggestion, or in case there's already an Addon, feel free to link.

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It looks as if you've already done most of this, but for the sake of completeness, trying to keep the steps minimal from the worst case:

To place the tetrahedron's origin at its centroid

  • In Object Mode, tetrahedron selected, ShiftAltO > 'Origin to Center of Mass'

To place the cone's origin at its point

  • In Edit mode, select the point vertex
  • ShiftS > 'Cursor to Selected'
  • In Object Mode, ShiftAltO > 'Origin to 3D Cursor'

To place the cone's point at the centroid of the terahedron

  • In Object Mode, tetrahedron selected, ShiftS > 'Cursor to Selected'
  • Cone selected, ShiftS > 'Selection to Cursor'

TL;DR, cut to the chase....

To align the cone to one of the vertices of the tetrahedron

(given you have created a vertex at the center of the cone's base, and having centered the cone to the tetrahedron, as above)

  • Set Pivot to '3D Cursor', Snap to 'Active' and 'Vertex'.
  • Object Mode, ShiftS 'Cursor to Selected' ( either cone or tetrahedron, to put the cursor at the cone's point)
  • Edit Mode, select all vertices of the cone, make the base-center vertex active.
  • In each axis in turn, RX,RY,RZ, snap the active vertex in rotation to the desired corner of the tetrahedron.

To move the base of the cone to one of the vertices of the tetrahedron

  • With preceding step taken, S scale the base to the corner, snapping to the active base-center vertex.

(You don't actually have to create a vertex at the center of the base of the cone .. instead of setting the snap to 'Active' you can set it to 'Center' and snap the cone's base as a whole, to the corner of the tetrahedron.)

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  • $\begingroup$ I believe I've done everything per instruction, even tried Center instead of Active, but it doesn't stick. Here's the file, to inspect <img src="https://blend-exchange.giantcowfilms.com/embedImage.png?bid=5745" /> from this point I'm rotating on X, but snapping doesn't occur, even though I'm certain the base center vertex should coincide with tetrahedron corner. Thank you for responding. $\endgroup$
    – t8ja
    Jan 14, 2019 at 16:46
  • $\begingroup$ Works for me... :( .. I got a perfect snap in your file (which arrived slightly out)- the height of your cone is spot on . You can't guarantee a snap to position in the first two rotations - only orientation in those dimensions. The last rotation should take you there. It helps to look down the axis you're rotating around.. I generally have the snap magnet set to off, and use ctrl to wake it up. Hover over the target until the snap circle is visible. I'm in 2.97? $\endgroup$
    – Robin Betts
    Jan 14, 2019 at 19:02
  • $\begingroup$ What do you mean by first two rotations ? I press R then X to constrain, and while rotating around, the cone gets into weird, seemingly random positions, although they're always the same depending on which snap option is chosen. I have the same version 2.79. $\endgroup$
    – t8ja
    Jan 14, 2019 at 19:50
  • $\begingroup$ maybe it has something to do with coordinates, because when I go into "Edit mode" on the cone, it shows me the original/spawn coordinates, not the actual coordinate of the vertex (for every vertex on the circle it's showing z=-1 while the other two are varying). $\endgroup$
    – t8ja
    Jan 14, 2019 at 20:11
  • $\begingroup$ I created a new cone, did the same thing as last time, but now it's working and the coordinates are correct (maybe I accidentally pressed something). Thank you for helping, and maybe you can explain this coordinate discrepancy (what did I press) ? $\endgroup$
    – t8ja
    Jan 14, 2019 at 20:42

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