For most people, the word “polyhedron” conjures up an image of a cube, a tetrahedron, or something similar—a solid figure with flat faces. If the polyhedron is regular, each face has the same size and ...

Consider what happens when a vertex of one tetrahedron pierces the face of a second tetrahedron to form a new, more complicated polyhedron. In the resulting geometric form, one triangular face has a ...

Mathematics Teaching in the Middle School (MTMS) is an official peer-reviewed journal of the National Council of Teachers of Mathematics and is intended as a resource for middle school students, ...

From their many gadgets to each department’s logos, The Odd Squad frequently finds and uses 2-dimensional (2D) and 3-dimensional (3D) shapes to help solve their investigations. In this activity, your ...

Lattice-free sets a n d their applications for cutting-plane methods in mixed-integer optimization have been studied in recent literature. The family of all integral lattice-free polyhedra that are ...