- Given a winged-edge representation of a solid, design algorithms
to answer the following queries:
- list all edges that contain a given vertex
- list all faces that contains a given vertex
- list all vertices and edges of a given face

- Find the winged-edge data structure of a cube.
- Find the winged-edge data structure of the following solid:
- Find the winged-edge data structure of the following solid:
- Verify Euler-Poincaré formula with the following polyhedra.
List the number of vertices, edges, faces, loops, shells and
holes.
- Use Euler operators to construct the following polyhedra: (1) a cube, (2) a cube with "pothole" and (3) a cube with a penetrating hole. Figures for the last polyhedra can be found in the winged-edge problems.
- One can define a new operator
**MEFL**in the Make group. This operator add an edge, a face and a loop. In general, this new edge subdivides a face into two, thus creating a new face and a new loop. In the following, the left one is a cube with vertices and edges of the top face shown. The right one is the result of apply an**MEFL**to the top face by adding an diagonal edge. The original square face is replaced by two triangles and**F**is increased by one. Similar,**L**is also increased by 1. Note that the value of the Euler-Poincaré formula does not change.One can use this operator

**MEFL**to subdivide all faces into triangles.Use

**MEKL**and**MEFL**to make all faces of a cube with a penetrate hole triangles. In the final result, do you have to worry about loops? - Starting with nothing, use Euler operators to construct a cube.