Elongated Triangular Gyrobicupola
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Elongated Triangular Gyrobicupola
Elongated triangular gyrobicupola
TypeJohnson
J35 - J36 - J37
Faces2+6 triangles
2x6 squares
Edges36
Vertices18
Vertex configuration6(3.4.3.4)
12(3.43)
Symmetry groupD3d
Dual polyhedron-
Propertiesconvex
Net

In geometry, the elongated triangular gyrobicupola is one of the Johnson solids (J36). As the name suggests, it can be constructed by elongating a "triangular gyrobicupola," or cuboctahedron, by inserting a hexagonal prism between its two halves, which are congruent triangular cupolae (J3). Rotating one of the cupolae through 60 degrees before the elongation yields the triangular orthobicupola (J35).

A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.[1]

## Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[2]

${\displaystyle V=({\frac {5{\sqrt {2}}}{3}}+{\frac {3{\sqrt {3}}}{2}})a^{3}\approx 4.9551...a^{3}}$

${\displaystyle A=2(6+{\sqrt {3}})a^{2}\approx 15.4641...a^{2}}$

## Related polyhedra and honeycombs

The elongated triangular gyrobicupola forms space-filling honeycombs with tetrahedra and square pyramids.[3]

## References

1. ^ Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics, 18: 169-200, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603.
2. ^ Stephen Wolfram, "Elongated triangular gyrobicupola" from Wolfram Alpha. Retrieved July 25, 2010.
3. ^ http://woodenpolyhedra.web.fc2.com/J36.html