All Questions

The paper Dividing a polygon into two similar polygons proves that there are only three families of polygons that are irrep-2-tiles (can be subdivided into similar copies of the original). Right ...

If such a pyramid exists, could someone provide the coordinates of its vertices?

Consider a Euclidean tetrahedron with lengths of edges $$ l_{12}, l_{13}, l_{14}, l_{23}, l_{24}, l_{34} $$ and dihedral angles $$ \alpha_{12}, \alpha_{13}, \alpha_{14}, \alpha_{23}, \alpha_{24}, \...

Question : Letting $S{^\prime}$ be the area of the inner pentagon made by the five diagonals of a convex pentagon whose area is $S$, then find the max of $\frac{S^\prime}{S}$.     ...

Define the caliper diameter of a polyhedron as follows: Let $P_1$ and $P_2$ be two planes both of which are parallel to the x axis such that the perpendicular distance between $P_1$ and $P_2$ is the ...

I have a frustum (truncated pyramid defined by six planes) and I need to compute a bounding sphere for this frustum that's as small as possible. I can choose the centre of the sphere to be right in ...