The shape you are looking for is known as a truncated tetrahedron.
A truncated tetrahedron is a three-dimensional geometric figure that can be formed by truncating (or slicing off) the vertices of a regular tetrahedron. This process transforms the triangular faces of the tetrahedron into hexagonal faces while introducing new triangular faces at the positions of the truncated vertices.
This type of polyhedron has:
- 6 vertices: This is because the original tetrahedron has 4 vertices, and each vertex is replaced by a triangular face, adding 2 more vertices, resulting in 6 vertices in total.
- 9 edges: The truncation process results in a net increase of edges. The original tetrahedron has 6 edges, and the new edges created from the triangular faces add an extra 3 edges, totaling 9 edges.
- 5 faces: A truncated tetrahedron has 4 triangular faces (from the tetrahedron) and 1 hexagonal face (created from truncating the tetrahedron), summing up to 5 faces.
In summary, a truncated tetrahedron is an interesting polyhedron with distinct geometric properties, perfectly fitting the criteria of having 6 vertices, 9 edges, and 5 faces.