In geometry, the sphenomegacorona is a Johnson solid with 16 equilateral triangles and 2 squares as its faces.

The sphenomegacorona was named by Johnson (1966) in which he used the prefix spheno- referring to a wedge-like complex formed by two adjacent lunes—a square with equilateral triangles attached on its opposite sides.

The suffix -megacorona refers to a crownlike complex of 12 triangles, contrasted with the smaller triangular complex that makes the sphenocorona.

[1] By joining both complexes, the resulting polyhedron has 16 equilateral triangles and 2 squares, making 18 faces.

[2] All of its faces are regular polygons, categorizing the sphenomegacorona as a Johnson solid—a convex polyhedron in which all of the faces are regular polygons—enumerated as the 88th Johnson solid

88

.

[3] It is an elementary polyhedron, meaning it cannot be separated by a plane into two small regular-faced polyhedra.

[4] The surface area of a sphenomegacorona

is the total of polygonal faces' area—16 equilateral triangles and 2 squares.

The volume of a sphenomegacorona is obtained by finding the root of a polynomial, and its decimal expansion—denoted as

ξ

{\displaystyle \xi }

With edge length

, its surface area and volume can be formulated as:[2][5]

=

)

a

2

≈ 8.928

2

= ξ

a

3

≈ 1.948

{\displaystyle {\begin{aligned}A&=\left(2+4{\sqrt {3}}\right)a^{2}&\approx 8.928a^{2},\\V&=\xi a^{3}&\approx 1.948a^{3}.\end{aligned}}}

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

{\displaystyle {\begin{aligned}&\left(0,1,2{\sqrt {1-k^{2}}}\right),\,(2k,1,0),\,\left(0,{\frac {\sqrt {3-4k^{2}}}{\sqrt {1-k^{2}}}}+1,{\frac {1-2k^{2}}{\sqrt {1-k^{2}}}}\right),\\&\left(1,0,-{\sqrt {2+4k-4k^{2}}}\right),\,\left(0,{\frac {{\sqrt {3-4k^{2}}}\left(2k^{2}-1\right)}{\left(k^{2}-1\right){\sqrt {1-k^{2}}}}}+1,{\frac {2k^{4}-1}{\left(1-k^{2}\right)^{\frac {3}{2}}}}\right)\end{aligned}}}

under the action of the group generated by reflections about the xz-plane and the yz-plane.