  Mixed elements meshes based on the modified octree approach contain several
co-spherical point configurations. While generating Delaunay tessellations to
be used together with the finite volume method, it is not necessary to
partition them into tetrahedra; co-spherical elements can be used as final
elements. This paper presents a study of all co-spherical elements that appear
while tessellating a 1-irregular cuboid (cuboid with at most one Steiner point
on its edges) with different aspect ratio. Steiner points can be located at any
position between the edge endpoints. When Steiner points are located at edge
midpoints, 24 co-spherical elements appear while tessellating 1-irregular
cubes. By inserting internal faces and edges to these new elements, this number
is reduced to 13. When 1-irregular cuboids with aspect ratio equal to
$\sqrt{2}$ are tessellated, 10 co-spherical elements are required. If
1-irregular cuboids have aspect ratio between 1 and $\sqrt{2}$, all the
tessellations are adequate for the finite volume method. When Steiner points
are located at any position, the study was done for a specific Steiner point
distribution on a cube. 38 co-spherical elements were required to tessellate
all the generated 1-irregular cubes. Statistics about the impact of each new
element in the tessellations of 1-irregular cuboids are also included. This
study was done by developing an algorithm that construct Delaunay tessellations
by starting from a Delaunay tetrahedral mesh built by Qhull.
