Only theoretically. A "point" takes up some space, but obviously they are used on the assumption that a "point" takes up no space at all. This assumption makes it difficult for them to realistically exist.
true
true
A cone needs a three dimensional space in which to exist but it's not a solid, it's a two dimensional surface.
Cone
A triangle is a two dimensional shape with three straight lines and three vertices. A sphere is a three dimensional object with no straight lines and no vertices and such that every point on its surface is a constant distance from a fixed point. It is not possible to have a triangle sphere.
Yes, it does exist.
true
true
true
The term "statue" is used for three-dimensional works of art. Of course, two-dimensional works of art exist, but they are not usually called "statues".
A 3D triangle
There are a number of three dimensional shapes. These include the cube, the square pyramid, the prism, as well as the rhombohedron.
vertex
A cone needs a three dimensional space in which to exist but it's not a solid, it's a two dimensional surface.
A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space.
Presumably, the "three dimensional triangular plane" is actually a two dimensional plane which is "tilted" with respect to the axes. The point of intersection is simply the coordinates of the solution to the simultaneous equations for the line and the plane.
The location of a point in 3-dimensional space.