5
$\begingroup$

I hope this is not too trivial for this forum. I was wondering if someone has come across this polytope.

You start with the rhombic dodecahedron, subdivide it into four parallellepipeds, enter image description here

and then fill the space between the four parallellepipeds with a tetrahedron, six parallellepipeds and four prisms (hopefully I counted correctly), so as to obtain a convex polytope.

Does this have a name? could someone provide a link to a picture?

Improve this question
$\endgroup$
0

4 Answers 4

Reset to default
3
$\begingroup$

Is this it?
           Rhombic Dodecahedron + Tetrahedron

Improve this answer
$\endgroup$
3
  • $\begingroup$ wow thanks. i think so, although it would help a lot if it could be seen from other perspectives, or even exploded according to the above subdivision. $\endgroup$
    – Camilo Sarmiento
    Commented Feb 18, 2013 at 8:47
  • $\begingroup$ This doesn't look right to me. I would expect faces that are adjacent to equilateral triangles to all be rectangles. In your left picture, they look more like rhombi... $\endgroup$
    – André Henriques
    Commented Feb 24, 2013 at 21:45
  • $\begingroup$ @André: I don't doubt you. I formed this as the Minkowski sum of a rhombic dodecahedron and a regular tetrahedron, but perhaps I did not scale one with respect to the other appropriately. Cannot check now... $\endgroup$
    – Joseph O'Rourke
    Commented Feb 25, 2013 at 0:44
7
$\begingroup$

It's the Minkowski sum of the rhombic dodecahedron with a regular tetrahedron. (The rhombic dodecahedron is it self the Minkowski sum of four segments).

Improve this answer
$\endgroup$
1
  • $\begingroup$ indeed. have you casually seen a picture of it with the decomposition written in the question? $\endgroup$
    – Camilo Sarmiento
    Commented Feb 16, 2013 at 16:13
3
$\begingroup$

It seems to ressemble the "Self-Dual Icosioctahedron #4" :

http://dmccooey.com/polyhedra/SelfDualIcosioctahedron4.html

Some code:

sage: P = polytopes.rhombic_dodecahedron()
sage: Q = polytopes.tetrahedron()
sage: R = P.minkowski_sum(Q)
sage: R.f_vector()
(1, 28, 54, 28, 1)
sage: R.plot()
Improve this answer
$\endgroup$
0
$\begingroup$

The above mentioned Minkowski sum is just an example of Alicia Boole Stott's expansion operation(s), cf. https://en.wikipedia.org/wiki/Expansion_(geometry)

--- rk

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .