Since Ludwig Justi’s 1902 dissertation “Konstruierte Figuren und Köpfe unter den Werken Albrecht Dürers” there have been no further studies on how the Nuremburg master structured heads and filled in their forms.  Based on the Head of a Man attributed to him, I have re-examined the issue.  Begun in 2016, this study corrects Justi’s findings by developing further his insufficiently elaborated first beginnings.
It has long been known that the Head of a Man was made “aus dem Maß” (to measure).  But just how this was done was inadequately accounted for by Justi.  In fact, the painting contains a complex system of formal arrangement based on mathematically quantifiable magnitudes. Indeed, it would appear that in comparison with other works by Dürer, the painting occupies a key position in his method of (head) construction.
In addition to the Head of a Man, I will consider purely fictive constructed heads, self-portraits, and portraits of both anonymous and identified individuals by Dürer’s hand. These are embedded in a number of traditions that the artist knew and drew from. Evidently, he also took his bearings from contemporary Italian painting. Dürer’s constructions are a synthesis of old and new art on the threshold from the Middle Ages to the Renaissance.
Provisionally it can be stated that before the commencement of his systematic studies of proportion and until the end of his life Dürer composed the organic structure of heads / faces in a geometrically planar manner that remained technically the same. In this he did not differentiate between a frontal orientation or a head turned to the side.
For each pictorial task he found a new approach, which built upon a basic pattern. His drawing instruments of compass and straight edge (ruler)  assigned positions to the components of the heads and faces, determined their relative positions, and provided contours. More than previously assumed, Dürer strove to unify nature study and artistic ideal. The extent, the precision, and the variability of his constructions are astonishing.
 Ludwig JUSTI, Konstruierte Figuren und Köpfe unter den Werken Albrecht Dürers (Leipzig, 1902); cf. Georg WOLFF Mathematik und Malerei (Wiesbaden 1925), esp.: "Idealfiguren der Porträtmalerei", 78-81.
Attributions of the painting to Dürer: Fedja ANZELEWSKY, Albrecht Dürer: das malerische Werk, 2 vols. (2nd revised edn., Berlin 1991), vol 1, 246–47, vol. 2,
plates 142–44; Campbell DODGSON, ‘Notes on Dürer’, Burlington Magazine 39 (1921), 177–78, 180–81, 183–84, plate I.A, plate II.B; Max J. FRIEDLÄNDER, ‘Zur Auktion der Sammlung M. v. Nemes, 1.
Die Gemälde’, Pantheon VII (1931), 141–46, here: 142–43; Friedrich WINKLER, Dürer. Des Meisters Gemälde, Kupferstiche und Holzschnitte, (Klassiker der Kunst in Gesamtausgaben, vol. 4) (4th
revised edn., Stuttgart / Berlin 1934, 92 and 420; Hans TIETZE / Erika TIETZE-CONRAT, Kritisches Verzeichnis der Werke Albrecht Dürers, vol. 2.1: Der reife Dürer. Von der venezianischen Reise
im Jahre 1505 bis zur niederländischen Reise im Jahre 1520 nebst Nachträgen aus den Jahren 1492 bis 1505 (Augsburg, 1937), 118, no. 660, fig. 279; (with reservations) Erwin PANOFSKY Albrecht
Dürer, 2 vols. (3rd. edn. Princeton, 1948), vol. 2, 19, no. 94; Konrad EBERLEIN, Albrecht Dürer (3rd edn., Reinbek bei Hamburg, 2011), 57.
from FRIEDLÄNDER (1931), 142. The discussion about construction was begun by Dodgson (1921).
The Head of a Man is a rarely appreciated painting that has to date been shown twice in exhibitions, in 1928 and in 1957.  Campbell Dodgson listed it as a work by Dürer in 1921 while it was in a London collection. Prompted by the work’s strict frontality and “cold, impersonal character” already at the time he discussed a schema inscribed in the head. He consulted Ludwig Justi, who had been awarded his doctorate in 1902 with a dissertation on “Konstruierte Figuren und Köpfe unter den Werken Albrecht Dürers” (Constructed figures and heads among the works of Albrecht Dürer). 
Erwin Panofsky wanted an attribution to Dürer to be confirmed by an x-ray analysis of the work.  When overpaintings were removed, the majority of art historians were convinced, such as Fedja Anzelewsky, especially since infrared reflectograms had uncovered the underdrawing in places.  Among the critics, Matthias Mende and Norbert Wolf, for example, cite no sufficient reasons for their deattributions. 
The Head of a Man is in the form of a bust that almost fills the picture space against a dark background. The large size of the en face head and the unvarying black, which also incorporates the outer clothing, endows the unidentified countenance with a strong presence. The work is presumably a study: the support of the otherwise well-preserved painting is merely a thin panel of wood to which parchment has been attached.
The man’s face has a warm complexion with a healthy skin colour and red cheeks as well as a few shiny spots. In addition to the eyebrows, a few white hairs among the stubble betray an advancing middle age, as do a few strands in the ash-blonde pageboy hairstyle, to which little graphic effort has been devoted.
The alert, concentrated-looking eyes are greenish-brown and display the reflection of a mullion and transom window on the cornea with its mirror-image reflection in the iris, typical of Dürer.  The facial features, lit from the left and carefully modelled with light and shadow are slightly asymmetrical, and one eye is depicted as smaller, giving them overall an even more true-to-life effect.
There are virtually no deviations in the execution of the painting from the underdrawings concentrated on the eyes, nose, mouth, and contour of the chin. Many lines can be seen through the paint layer.
The left eye (from the perspective of the viewer) was lowered a bit, the hair ‘grew’, and the wings of the nose were widened. They were originally positioned along a vertical line to the tear ducts of the eyes. Also, the original design of the upper lip of the mouth, which is relatively small in comparison to the wide chin and neck and slightly ‘opened’ by a brushstroke, was originally a bit narrower.
Anyone looking at the image more carefully discovers two ‘markings’: a vertical stroke divides the tip of the nose in the middle, and along the part of the hair there is a painted groove or
notch. These points support for the assumption that this is a constructed head. Through them runs the central line of a linear grid deriving from a division into three equal sections, taken over
from antiquity from the Roman architect Vitruvius and common during Dürer’s time. 
A complex geometric system is linked to the proportion diagram, which was created with a compass and straight edge in numerical relationships. This webpage created for the Milan exhibition Dürer and the Renaissance between Germany and Italy gives an idea of – through recreations – of Dürer’s construction process under the heading “Geometricized heads”.
 1928 at the Germanisches Nationalmuseum on the 400 anniversary of Dürer’s death and in 1957 in New York.
 Campbell DODGSON, 'Notes on Dürer', in Burlington
Magazine 39 (1921), 177-178, 180-181, 183-184, plate I.A, plate II.B.
 Erwin PANOFSKY, Albrecht Dürer, 2 vols, (3rd. edn., Princeton, 1948), vol. 2, 19, no. 94.
 Fedja ANZELEWSKY, Albrecht Dürer: das malerische Werk,
2 vols. (2nd revised edn., Berlin, 1991), vol. 1, 246–47, vol. 2, plates 142–44; additional attributions, for example, by Max J. FRIEDLÄNDER, ‘Zur Auktion der Sammlung M. v. Nemes, 1. Die
Gemälde’, Pantheon VII (1931), 141–46, here 142–43.3.
 Matthias MENDE, ‘Albrecht Dürer’ in Saur. Allgemeines Künstlerlexikon, Bd. 30 (2001), 295-306. Norbert Wolf, “Albrecht Dürer (Munich, Berlin, London, New York, 2010), 280, FW 14.
 W. REITSCH, 'Das Dürer-Auge', in: Marburger Jahrbuch für Kunstwissenschaft 4 (1928), 165-200.
 VITRUVIUS, Zehn Bücher über Architektur (De Architectura libri decem), trans. into German and with commentary by Curt Fensterbusch (Darmstadt, 1996), III.1.2. [in English: Vitruvius, The Ten Books on Architecture, trans. Morris Hickey Morgan (Cambridge, 1914).]
... will be given later ...
In 1921 the painting Head of a Man was in the collection of Mr S. Wilensky in London, where Campbell Dodgson became acquainted with it and identified it as a work by Dürer. The head has been considered constructed since its discovery. From London the work ended up in Munich in the possession of artist, writer, collector, and art dealer Franz Naager (1870–1942). He exhibited it in his room on Brienner Straße (the former location of the Schack Galerie). Naager experienced financial difficulties and had to sell it. The next owner was the Hungarian industrialist, art collector, and patron Marczell von Nemes (1866–1930), who had his residence at Schloss Tutzing on Lake Starnberg (the present-day Evangelische Akademie).
The Head of a Man was exhibited at the Germanisches Nationalmuseum in Nuremberg in 1928 at the exhibition commemorating the 400th anniversary of Dürer’s death. After Nemes' death, the art dealer Silberman (Vienna, with a branch in New York) auctioned the painting in Munich on 16 June 1931. The auction of the Nemes estate was carried out by the galleries of Paul Cassirer (Berlin), Hugo Helbing (Munich), and Mensing & Son (Frederik Muller & Co.), Amsterdam. The image remained in the possession of the Gallery Elkan and Aris Silberman Inc. in New York, until being sold to the industrialist Hickox. Mr and Mrs Charles Hickox lent it to the Silberman Gallery in 1957 for the exhibition "Art unites Nations" on the tenth anniversary of the United Nations in New York.
This would be the next to last public exhibition of the work for a long time. Later the Head of a Man was incorporated into the Barker Welfare Foundation, founded by Catherine Barker Hickox (1896–1970). The foundation passed it along to the Art Institute of Chicago on loan in 1973. In January 1985 the work was auctioned by Sotheby’s in New York and returned to Germany (under private ownership).