Thus, the fourth vertex is $\boxed{(0,1,1)}$.

Tue, 21 Apr 2026 13:42:58 +0000

The Essential Role of the Fourth Vertex: Why $oxed{(0,1,1)}$ Matters in 3D Geometry In the fascinating world of 3D geometry, understanding vertex positioning is crucial when analyzing polyhedra and spatial relationships. One such pivotal point often arises in coordinate-based proofs and constructions—specifically, the vertex $oxed{(0,1,1)}$. This point, nestled within the coordinate framework of three-dimensional space, plays a significant role in defining structures like tetrahedrons and convex hulls. So, why is the fourth vertex labeled $oxed{(0,1,1)}$ so important? Let’s explore. ### The Geometry Behind the Coordinates In Cartesian 3D space, every point is defined by three coordinates: $x$, $y$, and $z$. The vertex $oxed{(0,1,1)}$ occupies a unique position: its $x$-coordinate is 0, while $y$ and $z$ are both 1. This places the point precisely halfway between the positive $y$-axis and $z$-axis, elevated slightly in both directions from the origin. Its location embodies symmetry and utility, offering a foundational anchor in frameworks involving planes, edges, and faces.