The Schmitt-Conway biprism, also called an SCD tile or Schmitt-Conway-Danzer tile, is a convex polyhedron formed by joining two triangular prisms along a common rhombus face. It is a convex modification of Schmitt's nonconvex space-filling tile (Baake and Frettlöh 2005).
Copies fit into planar layers, with successive layers rotated through an angle 
.
When 
is an irrational number and only translations
and rotations of the tile are allowed, the resulting
tilings have no nonzero translational symmetry. Allowing
both the tile and its mirror image also permits periodic tilings
(Baake and Frettlöh 2005).
Some of the nonperiodic tilings have a screw symmetry, combining a rotation about an axis with a translation along it. Such a symmetry does not contradict nonperiodicity, which excludes pure translations. This differs from the quaquaversal tiling, whose unmarked triangular prism admits periodic tilings even without mirror images.
