Dihedral — where it appears
Named by 5 essays across 3 fields — each of them below, with the objects they name alongside it.
Two mirrors make one turn
Reflect a point in two mirrors meeting at 36° and the images arrive nine at a time, every one of them on a single circle about the line where the mirrors meet, to 4 × 10⁻¹⁶ m. The rule taught for the count — three hundred and sixty over the angle, less one — is right at six of nine angles tried and wrong at the rest, because it is a rule about angles that divide a half turn and it is quoted for angles that divide a whole one.
The corner that answers every eye
Three mirrors at right angles compose into the point inversion, so a ray entering leaves antiparallel to itself whatever direction it arrived from — a picture surface with no correct viewpoint because every viewpoint is correct. Tilt one face half a degree and the worst returning ray is out by exactly one degree, twice the error; the best is out by a twelfth of it, which is why a tolerance quoted from one measured ray is a statement about that ray.
Two mirrors show fewer images than they make
Two mirrors at 55° generate seventy-one images of a point and an eye between them can reach six. The count the field teaches — three hundred and sixty over the angle, less one — is out by as much as sixty-six against the orbit and never by a whole image against what a viewer standing on the bisector actually sees. It is a correct rule about the eye, quoted as a rule about the mirrors.
The anamorph that crosses a corner
Cast one design onto a floor and the wall at the end of it, from one eye. Each plane gets a collineation of its own; the two agree on the line where the planes meet, exactly, because a point of that line is a point of both. What they do not agree about is scale — the design runs 7.8 times its own size along the floor and 2.0 times up the wall, and the jump at the join is a factor of 3.9.
The room a divergent picture is a photograph of
A divergent construction depicts a rectangle on a plane leaning toward the camera, and the splay alone sets how far — 36.3° at a splay of 1.32. Stand a second such construction on the first one's far edge, as a wall, and the two recovered planes meet at 6.9°, not at the right angle a real room's corner would need.
Named alongside it
The objects these essays reach for when they reach for this one.
IsometryReflectionFixed pointHandednessPicture planeStation pointTaught and unmeasuredViewing positionVirtual imageAnamorphosisArcminuteCamera tilt