Unity3D - 3d Point (vector3) within cube-ish shape defined using vector3 points

Question

I am generating a cube-ish shape using four points and the thickness of the cube. The thickness of the cube and a the forwards direction are used to generate the points further out on the z-axis thus producing a cube rather than a flat square.

I am trying to determine whether the shape is intersecting with another. The easiest way i thought to do this was to check whether any of the corner points are inside the other shape or a point half way along an edge (i.e. a point between two corner points).

I'm struggling to create a method that can accurately determine whether a given point is inside the shape.

I've tried the following based on Unity's Rect.

public bool ContainsPoint(Vector3 point)
        {
            bool x = (point.x >= lowerBottomLeft.x && point.x <= upperBottomRight.x);
            bool y = (point.y >= UpperBottomLeft.y && point.y <= upperTopLeft.y);
            bool z = (point.z >= UpperBottomLeft.z && point.z <= lowerTopLeft.z); 

            if (x && y && z)
            {
                return true;
            }
            return false;
        }

Here's how i create the shape.

private void ConfigureHandBounds(Vector3 topL, Vector3 topR, Vector3 bottomL, Vector3 bottomR, Vector3 dir, float depth)
        {
            this.height = depth;
            this.direction = dir;

            upperTopLeft = topL;
            upperTopRight = topR;
            upperBottomLeft = bottomL;
            upperBottomRight = bottomR;

            //Calculate lower positions
            lowerTopLeft = (upperTopLeft + (dir.normalized * height));
            lowerTopRight = (upperTopRight + (dir.normalized * height));
            lowerBottomLeft = (upperBottomLeft + (dir.normalized * height));
            lowerBottomRight = (upperBottomRight + (dir.normalized * height));

            center = (lowerBottomLeft + upperTopRight) * 0.5f;
        }