Muqarnas

About Muqarnas

Look up beneath the dome of the Hall of the Two Sisters at the Alhambra in Granada, built during Muhammad V's second reign as part of the Patio de los Leones program (begun 1362, the dome generally dated to 1362–1365), and the ceiling does not resolve into a single surface. A field of small concave cells — niches stacked into niches, each tier slightly offset from the one beneath — opens above the square reception room and contracts toward a central eight-pointed star at the apex. Sixteen lateral windows admit shifting light, so the cells appear to dissolve and reappear as the sun moves. Muqarnas is the three-dimensional architectural element built from this hierarchical stack of small prismatic units (cells, half-cells, and connectors) arranged in tiers that step inward from a base ring or squinch zone to a crowning point. Its earliest secure attestations are in eastern Iran and Iraq in the late tenth and early eleventh centuries, with the form developing rapidly across the Islamic world and reaching its mature forms in the Nasrid palaces of Granada (Hall of the Two Sisters, Hall of the Abencerrajes), the Cairene Mamluk mosques (the Mosque-Madrasa of Sultan Hassan, 1356–1363), the Persian Timurid and Safavid monuments (the portals and squinches of the Friday Mosque of Isfahan), and the great Ottoman mosques of Sinan (Süleymaniye 1550–1557, Selimiye Edirne 1568–1574). The element appears in domes, half-domes, squinches, pendentives, transition zones between square plans and circular domes, mihrab hoods, gateway portals, and cornices. It is built in carved stone, stucco over wood lath, cut brick, glazed tile, and — in the Maghrebi and Andalusian variant called mocárabe — gypsum plaster carved and assembled from prefabricated modules. The construction was governed by a flat plan-drawing tradition documented in the Topkapı Scroll, a fifteenth-century Persian roll preserved at Istanbul that records muqarnas projections as two-dimensional cell layouts from which the three-dimensional vault can be raised.

Mathematical Properties

A muqarnas vault is a three-dimensional fractal-like assembly drawn from a finite kit of small geometric units. Jamshīd al-Kāshī's *Miftāḥ al-Ḥisāb* (1427) names and gives area-and-volume formulas for the canonical units used in Timurid practice: the square cell (murabbaʿ), the rhombus or lozenge (muʿayyan), the almond (lawza, a kite-shaped quadrilateral), the biped (dhū qadamayn), the barley-kernel (jūz al-shaʿīr), and several connector tiles. Each unit has a concave inner face and a flat or convex back; each fits to its neighbors along edges of standardized length so that a tier of units forms a continuous ring offset inward from the tier below.

The full vault is not generated by a continuous mathematical surface. It is assembled by stacking these prefabricated units in tiers and projecting their arrangement onto a flat plan drawing. The Topkapı Scroll (Istanbul, c. fifteenth century) and the Tashkent Scrolls preserve dozens of such plans. Each plan shows the muqarnas as a two-dimensional pattern of small polygons (the projection of each cell onto the floor); the third dimension is implicit in the unit-type chosen for each polygon. This is the architectural-design equivalent of a knitting pattern: a flat document from which a three-dimensional object is built without ambiguity, provided the kit-of-parts is fixed.

The symmetry of the vault projection is typically dihedral. Hall-of-the-Two-Sisters-class domes use eight-fold (D8) symmetry; the central star is eight-pointed, and the tiers radiate from it. Mamluk-style mihrab-hood muqarnas often use four-fold or fold-symmetric layouts; Persian portal muqarnas frequently use sixteen-fold or twelve-fold layouts. The number of cells grows roughly as the square of the number of tiers — a four-tier vault has on the order of a hundred cells, a seven-tier vault several hundred.

Yvonne Dold-Samplonius and Silvia Harmsen's 2004 reconstructions, presented at the Nexus Network Journal conferences, demonstrated that al-Kāshī's flat-plan method generates buildable muqarnas vaults exactly when applied with the unit-coefficients he gives. The vault is not an after-the-fact approximation of a continuous dome; it is a discrete object specified to the same level of mathematical precision as a tessellation. The interior surface, taken as a whole, is not a smooth manifold — it has corners and edges everywhere, and the limit (if more and more tiers are added with smaller units) is not a sphere but a fractal-like surface of constant non-smoothness. This is structurally and visually the point of the form: the eye is denied a single resolution.

Architectural Use

Muqarnas appears across the full breadth of Islamic monumental architecture from the late tenth century forward. The earliest secure attestations are at modest sites in eastern Iran and Iraq: the Tomb of the Sāmānids at Bukhara (c. 943, with proto-muqarnas squinches), the Friday Mosque of Nayin (tenth century, stucco), and a small group of early-eleventh-century shrines in Iran and northern Iraq that Tabbaa cites in his 1985 essay as the earliest fully-developed muqarnas vaulting. From Baghdad and Cairo the form spread west and east rapidly.

In the Maghreb and al-Andalus, muqarnas (more often executed in carved gypsum plaster and called mocárabe) defines the great Nasrid spaces of the Alhambra at Granada: the Hall of the Two Sisters (the eight-pointed-star muqarnas dome over a square room, built during Muhammad V's second reign as part of the Patio de los Leones program begun in 1362, the dome generally dated to 1362–1365), the Hall of the Abencerrajes (the eight-pointed-star muqarnas dome over an octagonal drum, lit by sixteen lateral windows, in the same second-reign program), and the surrounding portico vaults of the Patio de los Leones. Earlier Maghrebi instances appear at the Bou Inania Madrasa in Fez (1351–1356) and the Qarawiyyīn Mosque additions.

In Mamluk Cairo, muqarnas takes on a heavier carved-stone idiom. The Mosque-Madrasa of Sultan Hassan (1356–1363, completed under the regents after Sultan Hasan's death in 1361) carries muqarnas portals of monumental scale; the four iwāns of its central courtyard have muqarnas cornices and squinches. The earlier Mosque of al-Aqmar (1125) and the Mausoleum of Imām al-Shāfiʿī (1211) preserve smaller-scale Fatimid and early-Ayyubid examples.

In the Persian Timurid and Safavid traditions, muqarnas dominates the great portal-iwān architecture. The Friday Mosque (Masjid-i Jāmiʿ) of Isfahan carries multiple phases of muqarnas in its mihrab dome (Saljuq and later) and entrance portals. The Bibi Khanum Mosque at Samarkand (1399–1404, Timur), the Shāh-i Zinda necropolis (fourteenth–fifteenth century), and the Shāh Mosque and Sheikh Lotfollah Mosque at Isfahan (1611–1638, Safavid Shah Abbas) all carry monumental muqarnas portals over fifteen meters tall.

In the Ottoman tradition, the architect Sinan deployed muqarnas in restrained classical idiom: the Süleymaniye Mosque in Istanbul (1550–1557) and the Selimiye Mosque at Edirne (1568–1574) carry muqarnas mihrab niches, capitals, and pendentive transitions. The form continues into the Indian Sultanate and Mughal traditions, the Central Asian khanate architecture, and contemporary Gulf and Maghrebi religious construction.

Construction Method

Muqarnas is built in five steps: the kit-of-parts is chosen, the flat plan is drawn, the bottom ring is set on the squinch zone, each subsequent tier is corbeled inward from the one beneath, and the apex is closed with a small star-shaped capstone or central element.

Step one — the kit. The architect chooses a finite set of unit shapes appropriate to the dynasty and material. In the Persian Timurid tradition that al-Kāshī codified (Samarkand, 1427), the kit includes the murabbaʿ (square), muʿayyan (rhombus), lawza (kite), dhū qadamayn (biped), and jūz al-shaʿīr (barley-kernel). In the Maghrebi mocárabe tradition the kit is somewhat different and the units are smaller. In Mamluk Cairo the units are larger and the kit is leaner. Each kit is internally consistent: every unit fits to every other along edges of standardized length.

Step two — the flat plan. The architect draws the muqarnas as a two-dimensional pattern on a flat surface (the floor of the workshop, a sheet of parchment, or a scroll). The plan shows the projection of every cell onto the floor of the room. Each polygon in the plan is labeled with its unit-type. The plan is a complete specification of the vault. The Topkapı Scroll preserves dozens of such plans without elevation drawings, because the elevation is implicit in the choice of unit.

Step three — the bottom ring. The lowest tier of cells is built on the squinch zone of the room (the eight or sixteen brackets that span the room's corners and transition from a square to a polygon). This ring is usually the largest and is structurally load-bearing in stone or brick construction.

Step four — successive tiers. Each subsequent tier is corbeled inward, with the cells in tier *n+1* offset from the cells in tier *n* such that their bases rest on the upper edges of the tier below. The cells in the upper tiers are smaller. The vault contracts as it rises. The horizontal projection of each tier is a smaller ring than the one below.

Step five — the apex. The vault closes on a central star configuration (the Hall of the Two Sisters at the Alhambra closes on an eight-pointed star with smaller cells radiating outward; many Mamluk vaults close on a small dome-let; Ottoman vaults close on a calligraphic medallion).

Materials vary by tradition. The Mamluks worked in carved stone for monumental portals and in stucco for interior squinches and mihrab hoods. The Persian Timurids and Safavids worked in stucco, glazed tile, and cut brick — often combining all three within a single portal. The Ottomans worked in carved stone with painted or gilded surfaces. The Maghrebi and Andalusian builders worked almost entirely in carved gypsum plaster, prefabricating cells in modular forms (the technique called mocárabe), and assembling them by mortar onto a wooden frame.

In every tradition the work is anonymous-guild. The architect is named only for the most royal commissions (Sinan for the Ottoman corpus; the al-Banna family for several Mamluk Cairene mosques; the unnamed Nasrid masters of the Alhambra). The craft was transmitted master-to-apprentice. Surviving artisan scrolls (Topkapı, Tashkent) record the geometry; surviving tax registers and waqf documents occasionally record the names of the master builders.

Spiritual Meaning

The theological reading most fully developed in the scholarly literature is Yasser Tabbaa's 1985 Ash'arite-atomist proposal. In the Ash'arite tradition that consolidated under the Sunni Revival of the eleventh century and was formulated by al-Bāqillānī (d. 1013), the world is not a Greek-style continuum sustained by inherent natures. It is a field of discrete atoms whose every accident — shape, color, position, motion, luminosity — is re-created at every instant by the direct will of God. The world is a flicker, not a continuum. Causation is divine custom, not necessity. A stone falls because God wills it to fall, and the regularity of falling is the regularity of God's habit, not of any internal property of the stone.

A muqarnas dome architecturally performs this cosmology. The vault overhead is not a single solid hemisphere. It is hundreds of small cells whose painted surfaces register light differently from instant to instant as the sun moves and the lateral windows admit changing light. The whole holds together as a vault, but the eye is never permitted to rest on a single surface. The dome flickers. The aggregate is held in being only by the continuous willing of God in the same way that the universe is.

This reading is contested. Some scholars (Behrens-Abouseif, Necipoğlu) emphasize that muqarnas spread well beyond Ash'arite intellectual centers — into Maliki Maghreb, into Twelver Shi'a Iran — and that the form survived theological shifts that should, on Tabbaa's account, have killed it. Others (Mohammed al-Asad, Sara Bonnemaison) read the form as primarily structural, decorative, and acoustic, with theological readings as later overlay. Both readings are in print. What is uncontested is that the muqarnas vault is a sustained meditation on the nature of surface, light, and unity-in-multiplicity — themes that map onto Islamic theology of *tawḥīd* (the divine unity beyond all created multiplicity) regardless of the specific Ash'arite-atomist framing.

What the form does *not* carry, in the documented scholarly tradition, is any claim to hidden inheritance. The Topkapı Scroll, the Tashkent Scrolls, and al-Kāshī's *Miftāḥ al-Ḥisāb* are open artisan-and-mathematician documents preserved in royal libraries because the patrons wanted them preserved. The geometry was transmitted master-to-apprentice in standard guild fashion. The theological reading was likewise published openly in treatises by al-Bāqillānī and others — the same texts taught in the madrasa system that the muqarnas-vaulted buildings often housed. The muqarnas vault is theologically charged public craft, openly transmitted.

Significance

The muqarnas vault is the Islamic architectural answer to a problem every domed building faces — how to transition from a square room to a round dome — and it answers the problem by refusing to smooth the transition at all. Where Byzantine architecture resolves the same junction through pendentives that flow continuously from the square corners to the drum, and where Roman architecture resolves it through coffered concentric rings, muqarnas multiplies the junction into a field of small cells that step inward in discrete tiers. The eye never lands on a single surface. The ceiling fractures into prisms and reassembles only when the sun shifts.

This structural choice carries theological weight in the reading proposed by Yasser Tabbaa in his 1985 essay "The Muqarnas Dome: Its Origin and Meaning," published in *Muqarnas III* under Oleg Grabar's editorship. Tabbaa traces the form to early-eleventh-century Baghdad and argues that its emergence corresponds to the rise of Ash'arite atomist-occasionalist theology, especially as formulated by al-Bāqillānī (d. 1013) and consolidating under the Sunni Revival of the eleventh century. In the Ash'arite view, the world is composed of atoms held in being moment by moment by direct divine willing; shape, color, and luminosity are accidents that God re-creates instant by instant. A muqarnas vault, broken into hundreds of small cells whose painted or stuccoed surfaces register light differently from second to second, performs this theology architecturally. The dome is not a single solid sphere overhead but a flickering aggregate held together by the same continuous act of divine willing that holds the universe together. Tabbaa's reading has been contested by scholars who emphasize the form's structural and acoustic functions over its theology, and Doris Behrens-Abouseif and others have shown that muqarnas spread well beyond the Ash'arite orbit. The debate is live; both readings are part of the literature.

What is not in dispute is the form's mathematical sophistication. Yvonne Dold-Samplonius, working from the Persian mathematician Jamshīd al-Kāshī's *Miftāḥ al-Ḥisāb* ("Key of Arithmetic," completed 1427 in Samarkand under Ulugh Beg), reconstructed how Islamic architects measured the volume and surface area of muqarnas vaults. Al-Kāshī decomposed the vault into a kit of named prefabricated units — squares, rhombuses, almonds (kite-shaped quadrilaterals), bipeds, and barley-kernels — and gave coefficients for the area and volume of each from sexagesimal approximations of square roots. The architect did not improvise the cells. He chose them from a finite vocabulary and projected the arrangement onto a flat plan that the masons then raised into three dimensions. The Topkapı Scroll (Istanbul, Topkapı Museum Library, MS H.1956), studied in depth by Gülru Necipoğlu in her 1995 monograph *The Topkapı Scroll: Geometry and Ornament in Islamic Architecture*, preserves dozens of such muqarnas plans alongside flat star-pattern designs.

The muqarnas vault is therefore a place where theology, mathematics, and craft converge in stone and stucco. It is one of the few architectural elements in the world that is at once a structural device, a geometric exercise, a light-modulator, and a confession of cosmology. The Nasrid courts at the Alhambra, the Mamluk mosques of Cairo, the Timurid portals at Samarkand, and the Ottoman mihrab-niches of Sinan are each working a different inflection of the same instrument.

Connections

Within Islamic architecture, muqarnas connects to mocárabe (the Maghrebi and Andalusian gypsum-plaster variant — see the separate page), to girih tile and the full Islamic star-pattern tradition (the Topkapı Scroll preserves muqarnas plans alongside girih designs, indicating a shared design culture), and to the squinch and pendentive traditions of late antique and Byzantine architecture from which the form structurally descends. Outside Islamic architecture, the closest cross-tradition resonance is to the Chinese dougong bracket cluster, where a stacked field of small wooden brackets steps outward to carry the eaves of a temple roof — a structurally different problem (tension and cantilever rather than dome transition) solved by a comparable strategy of breaking a single transition into many small units. The Indian temple shikhara is sometimes compared to muqarnas because both build a tall mass from many small repeated units, but the resemblance is surface only — the shikhara is solid masonry stacked into a curving silhouette, while muqarnas is hollow and concave throughout. The modern parallel is the parametric architecture of the late twentieth and early twenty-first century — work by Zaha Hadid, Foreign Office Architects, and others — in which a single complex surface is generated by combinatorial assembly of small parametrically-related units. Yvonne Dold-Samplonius and Silvia Harmsen's 2004 digital reconstructions at Nexus Network Journal made the parallel explicit by rebuilding historical muqarnas vaults in CAD. The form is also studied in contemporary acoustics: the broken concave surface of a muqarnas dome scatters sound rather than focusing it, and a major mosque dome made of muqarnas produces an even acoustic field rather than the focusing whisper of a smooth dome.

Further Reading

• Yasser Tabbaa, "The Muqarnas Dome: Its Origin and Meaning," *Muqarnas* 3 (1985): 61–74 — the canonical Ash'arite-atomist reading. Yvonne Dold-Samplonius, "Practical Arabic Mathematics: Measuring the Muqarnas by al-Kāshī," *Centaurus* 35 (1992): 193–242 — the canonical mathematical reconstruction. Gülru Necipoğlu, *The Topkapı Scroll: Geometry and Ornament in Islamic Architecture* (Getty 1995) — the scroll itself, with full reproductions of the muqarnas plans. Doris Behrens-Abouseif, *Cairo of the Mamluks: A History of the Architecture and its Culture* (American University in Cairo Press 2007) — for the Mamluk corpus including Sultan Hassan. Oleg Grabar, *The Alhambra* (Harvard 1978) — for the Hall of the Two Sisters and Hall of the Abencerrajes. Yasser Tabbaa, *The Transformation of Islamic Art During the Sunni Revival* (University of Washington Press 2001) — for the broader Sunni-Revival framing and for the dating of Hall of the Two Sisters within Muhammad V's second-reign program. Sheila Blair and Jonathan Bloom, *The Art and Architecture of Islam 1250–1800* (Yale 1994) — for the comparative regional picture. Eric Broug, *Islamic Geometric Patterns* (Thames & Hudson 2008) — for the related flat-pattern tradition and its construction logic.