In 3D modeling software like Autodesk 3ds Max, different object types allow for various levels of manipulation.
The question describes an object type that:
1. Is deformable.
2. Is a mesh object made up of triangular faces.
3. Provides controls for manipulation at three sub-object levels: vertex, edge, and face.
Let's consider the options in the context of 3ds Max:
(ë) (a) Element: In 3ds Max (especially for Editable Poly or Editable Mesh), "Element" is a sub-object selection level. It refers to a connected group of faces within a single object (e.g., if you have a teapot object made of a body, spout, handle, and lid as separate but connected mesh parts, each part can be selected as an "element"). It's a selection level, not an object type itself in the way the question implies.
(ì) (b) Keyframes: Keyframes are used in animation to define the state of an object or its parameters at specific points in time. They are part of the animation system, not a type of deformable geometric object.
(í) (c) Editable Mesh: An "Editable Mesh" object in 3ds Max is a fundamental type of deformable mesh. Its underlying geometry is composed entirely of triangular faces. It provides sub-object editing modes for:
(î) Vertex: Manipulating individual vertices.
(ï) Edge: Manipulating edges (which connect two vertices and are part of two adjacent triangular faces).
(ð) Face: Manipulating individual triangular faces.
(ñ) Polygon (co-planar faces, less direct than Editable Poly)
(ò) Element (connected group of faces).
This matches the description very well, particularly the "made up of triangular faces" and the sub-object levels.
(ó) (d) Editable Poly (Editable Polygon): An "Editable Poly" object is another, often more powerful and flexible, type of deformable mesh in 3ds Max. Its underlying geometry is composed of polygons (which can be triangles, quads, or n-gons). While it can be tessellated into triangles for rendering, its native structure supports polygonal faces. It also has sub-object levels like vertex, edge, border, polygon, and element. The key distinction from Editable Mesh is that Editable Poly works natively with polygons (quads, n-gons are common), while Editable Mesh fundamentally works with triangles.
The description "a mesh object made up of triangular faces" points directly to the fundamental nature of an Editable Mesh. While Editable Poly can also be manipulated at vertex, edge, and face (polygon) levels, its basic building blocks are polygons, which are then internally triangulated. Editable Mesh's visible faces are always triangles.
Given the emphasis on "triangular faces" as the composition, Editable Mesh is the more precise fit.
\[ \boxed{\text{Editable mesh}} \]