In
geometry, the sphenomegacorona is one of the
Johnson solids (J88). It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the
Platonic and
Archimedean solids.
Johnson uses the prefix spheno- to refer to a wedge-like complex formed by two adjacent lunes, a lune being a
square with
equilateral triangles attached on opposite sides. Likewise, the suffix -megacorona refers to a crownlike complex of 12 triangles, contrasted with the smaller triangular complex that makes the
sphenocorona. Joining both complexes together results in the sphenomegacorona.[1]
Cartesian coordinates
Let k ≈ 0.59463 be the smallest positive root of the
polynomial
Then,
Cartesian coordinates of a sphenomegacorona with edge length 2 are given by the union of the orbits of the points
under the action of the
group generated by reflections about the xz-plane and the yz-plane.[2]
The
surface area of a sphenomegacorona with edge length a can be calculated as:
^Timofeenko, A. V. (2009), "The non-Platonic and non-Archimedean noncomposite polyhedra", Journal of Mathematical Science, 162 (5): 720,
doi:
10.1007/s10958-009-9655-0,
S2CID120114341