Elongated triangular gyrobicupola

Elongated triangular gyrobicupola
Type	Johnson J35 - J36 - J37
Faces	2+6 triangles 2.6 squares
Edges	36
Vertices	18
Vertex configuration	6(3.4.3.4) 12(3.4^3)
Symmetry group	D3d
Dual polyhedron	-
Properties	convex
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 have regular faces but are not uniform (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]

$V=(\frac{5\sqrt{2}}{3}+\frac{3\sqrt{3}}{2})a^3\approx4.9551...a^3$

$A=2(6+\sqrt{3})a^2\approx15.4641...a^2$

Related polyhedra and honeycombs

Elongated triangular gyrobicupola forms space-filling honeycombs with Tetrahedron and Square pyramid.^[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

External links

• Eric W. Weisstein, Elongated triangular gyrobicupola (Johnson solid) at MathWorld