Trammid

The trammid is a theoretical geometric solid defined as a prismatoid formed by two congruent polygons placed in parallel planes and joined by corresponding vertices with parallelogram faces. The two bases are congruent and parallel; side faces are parallelograms; the top base is typically obtained from the bottom by a translation combined with rotation around an axis perpendicular to the bases, producing a twist.

Construction: Begin with base polygon P with n vertices; place a congruent copy Q in a plane parallel to P at height h; allow a rigid motion that can include translation and rotation about the normal vector. Connect each vertex of P with the corresponding vertex of Q by a quadrilateral face; the resulting polyhedron has V=2n vertices, E=3n edges, and F=n+2 faces (two bases plus n parallelogram sides).

Variants: If the second base is directly above and unrotated, the trammid reduces to a standard prism; if the second base is rotated, it is a twisted trammid. Larger rotations or offsets do not change the vertex/edge count but alter geometry of side faces.

Etymology and usage: The term “trammid” is not standard in formal geometry. It appears in some educational or speculative contexts as a name for a skewed prism; it should not be confused with the trammel (an ellipsograph) or other similarly named devices.

Applications: Used mainly as a pedagogical construct to illustrate prismatoid properties, symmetry considerations, and basic polyhedral topology; may inform computer graphics and architectural design for skewed prism-like forms.

See also: prism, antiprism, parallelepiped, skew prism.