pyramid
A pyramid fits the given description
The given description fits that of a triangular based pyramid which has 4 faces, 6 edges and 4 vertices
A vertex can be the corner of a polyhedron in which case at least three edges meet at a vertex.
An endpoint where two edges intersect on a polyhedron is called a vertex.
A Polyhedron is a closed plane figure whose faces are portions of planes. Prisms and pyramids are examples of Polyhedron's. While a Regular Polyhedron is a Polyhedron whose facces are all regular Polygons and whose Vertices are all alike. There are only five Regular Polyhedron's: Tetahedron , Octahedron , Icosahedron , Hexahedron , and Dodecahedron .To clarify, there are five known Platonic Solids: regular polyhedrons which are convex on all their vertices.The tetrahedron is also known as the triangular pyramid: a regular one has an identical equilateral triangle for each of its four faces. This is the one Platonic solid which is self-dual, as each face has three sides and each vertex joins three edges.The regular hexahedron is better known as the cube: each of its six faces is a square, and each vertex joins three edges. Its dual counterpart is the regular octahedron. In this case, each of its eight faces is three-sides (an equilateral triangle) and each vertex joins four edges. To picture the octahedron, think two square pyramids mated on their square faces, leaving only the triangular faces.Finally, there is the regular dodecahedron (12 faces), which is composed of regular pentagons (five sides). Each vertex again joins three edges. Its dual counterpart is the regular icosahedron. It has 20 triangular faces, and each vertex joins five edges.
There are an infinite number of such polyhedra. Starting with a tetrahedron (triangular base), the next up is the quadrilateral pyramid (quadrilateral base), then the pentagonal pyramid, the hexagonal pyramid and so on.
A pyramid fits the given description
polyhedron
A tetrahedron is a geometric solid with four triangular faces, six edges, and four vertices. It is a type of polyhedron with triangular faces meeting at each vertex.
A pyramid has a polygonal base with all other sides being triangles. As the Egyptians famously demonstrated, a common pyramid has a square base with four triangles meeting at a vertex, but any polygon - regular or irregular - can be used as the base of such a polyhedron.
pyramid
There are an infinite number of possible solutions. A tetrahedron and icosahedron are regular shapes. Then there is the triangular prism. A cuboid with one vertex cut off, a cube with 2 vertices cut off, 3 vertices etc. In fact, cutting off the vertex of any polyhedron in which three sides (faces) meet at the vertex will give a new triangular face.
The given description fits that of a triangular based pyramid which has 4 faces, 6 edges and 4 vertices
Pyramid
A pyramid seems to fit the description.
A polyhedron of which one face is a square, and the other faces are triangles with a common vertex.
For every polyhedron, there is a dual which is a polyhedron that has:a face where the first had a vertex,a vertex where the first had a face,the same number of edges.A self-dual polyhedron is a polyhedron whose dual is the same shape.All pyramids, for example, are self-dual.