What is the name of this convex polyhedron?

The top and bottom vertices are degree-$6$, spanning hexagons, which are zigzag connected in the band between the two hexagons. The faces are approximate isosceles triangles in this physical model.

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    $\begingroup$ I don't know whether it has a name but there's an interesting generalization. You can build something like this by adding pyramids to the top and bottom faces of an antiprism. All the faces can be isosceles. $\endgroup$ May 1, 2019 at 12:06
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    $\begingroup$ @EthanBolker: So perhaps a capped antiprism. $\endgroup$ May 1, 2019 at 12:10
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    $\begingroup$ I think we can go with Dennis, maybe? $\endgroup$
    – Asaf Karagila
    May 1, 2019 at 12:57
  • $\begingroup$ @AsafKaragila: According to @ zwim, apparently "Frank" is more apt. $\endgroup$ May 1, 2019 at 13:10
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    $\begingroup$ Pentahex polyhedera were extensively studied by Buckminster Fuller in relation to the design of geodesic domes. See his book, "Critical Path". When I was an engineering student at UC Berkeley in the early 1960's, he had a weekly show on local radio station KPFA. $\endgroup$ May 7, 2019 at 18:52

4 Answers 4


I believe it is a gyroelongated hexagonal bipyramid.


The example shown in the Wikipedia article uses equilateral triangles, which results in coplanar faces around the degree-6 vertices, but as you mention, the model uses isosceles triangles.


From http://rcsr.anu.edu.au/polyhedra

I entered $14$ vertices and $24$ faces, and it seems to be a C14 Frank Kasper polyhedron (seems to be named from chemist researcher...)

The degrees of vertices $5$ and $6$ correspond.



If I am right, the four extra faces make it a tetraicosahedron. But this is a generic term.


As already was said, all faces could be made the same isoceles triangle.

But alternatively the equatorial segment could be made a uniform hexagonal antiprism too. Then the emphasis would be more towards that antiprism than to those attached pyramids. Therefore you also could speak of a "bi-apiculated hexagonal antiprism".

--- rk


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