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A cone is a three-dimensional geometric shape with a circular base and a curved surface tapering to a point called the apex or vertex.

A cone has two parts that can be considered as vertices:

1. The apex or vertex, where all the slant edges meet.
2. The center of the circular base.

So, a cone has two vertices: the apex and the center of the circular base.

A polyhedron is a three-dimensional geometric figure with flat faces, straight edges, and vertices.

Out of the options provided, a cone is not a polyhedron.

• A cube is a polyhedron because it has flat faces, straight edges, and vertices.
• A prism is a polyhedron because it has flat faces, straight edges, and vertices.
• A cuboid is a polyhedron because it has flat faces, straight edges, and vertices.

However, a cone does not have flat faces; it has a curved surface. Therefore, a cone is not considered a polyhedron.

A triangular prism is a type of polyhedron with two triangular faces and three rectangular faces. Let's count the faces, edges, and vertices:

1. Faces:
   • Two triangular faces.
   • Three rectangular faces.

So, the total number of faces is 2 (triangular) + 3 (rectangular) = 5 faces.

2. Edges:
   • Each triangular face has 3 edges.
   • Each rectangular face has 4 edges.

So, the total number of edges is 2 (triangular faces * 3 edges per face) + 3 (rectangular faces * 4 edges per face) = 6 + 12 = 18 edges.

3. Vertices:
   • Each triangular face has 3 vertices.
   • Each rectangular face has 4 vertices.

So, the total number of vertices is 2 (triangular faces * 3 vertices per face) + 3 (rectangular faces * 4 vertices per face) = 6 + 12 = 18 vertices.

Therefore, a triangular prism has:

• 5 faces,
• 18 edges, and
• 18 vertices.

A triangular pyramid, also known as a tetrahedron, is a type of pyramid that has a triangular base and three triangular faces that meet at a single vertex.

A pyramid with a square base is called a square pyramid. It has a square base and four triangular faces that meet at a single vertex, which is directly above the center of the square base.