Glossary entry

Vesica Piscis

noun · / ˈvɛs.ɪ.kə ˈpɪs.kɪs / · sacred geometry construction · also: mandorla, almond, yoni

The lens-shaped overlap region between two circles of equal radius where each circle's centre lies on the other's circumference. The foundational construction of the Flower of Life and one of the most-used shapes in sacred geometry. Called the mandorla in Christian iconography where it surrounds figures of divine majesty. Width-to-height ratio of √3 to 1 (≈ 1.732 : 1). First formally documented in Euclid's Elements, Book I, Proposition 1, c. 300 BC.

By Sarah Chen · Last updated 15 May 2026

Construction

Draw a circle. Draw a second circle of the same radius such that its centre lies on the first circle's circumference. The two circles necessarily overlap; the lens-shaped area where they overlap is the Vesica Piscis. The two intersection points, together with either circle's centre, form an equilateral triangle (since all three sides equal the circles' radius).

Mathematics

The Vesica Piscis has a width-to-height ratio of √3 to 1 (≈ 1.732 : 1). The √3 ratio is one of the fundamental irrational ratios in classical geometry — it appears in equilateral triangles, regular hexagons, and the dynamic-symmetry root rectangles. Euclid uses the Vesica Piscis construction in Elements, Book I, Proposition 1, to prove the existence of an equilateral triangle from a given line segment — making the Vesica Piscis literally the first geometric construction in the western mathematical tradition.

The mandorla in Christian iconography

In Christian iconography, the Vesica Piscis is called the mandorla (Italian for "almond") and surrounds figures of divine majesty. Christ in Majesty (Christ Pantocrator) is the most common subject — depicted within a mandorla in Romanesque tympanum sculptures, Byzantine apse mosaics, Gothic stained-glass roundels, and Renaissance altarpieces. The Virgin Mary in glory is also frequently depicted within a mandorla. The mandorla represents the meeting of heaven and earth — the divine breaking through into material reality, framed by the geometric figure that represents the intersection itself.

Where it sits in sacred geometry

The Vesica Piscis is the geometric ancestor of nearly every other sacred geometry construction:

Seed of Life — adds 5 more circles using the same compass setting.
Flower of Life — extends the Seed through three concentric rings to 19 circles.
Metatron's Cube — derives from a 13-circle Fruit of Life subset.
Equilateral triangle — formed by the two intersection points and either circle centre.
Regular hexagon — six Vesica Piscis constructions arranged around a central point.

In Grid Maker Pro

Implemented as the Vesica Piscis overlay. Adjustable circle radius, line thickness, line colour, and orientation. The overlay can be rendered with the lens only (clean mandorla) or with the full circles visible.

Related terms

Sacred geometry — the broader category.
Flower of Life — the 19-circle extension built from the Vesica Piscis.

Citations

Euclid. Elements, Book I, Proposition 1. c. 300 BC.
Schiller, Gertrud. Iconography of Christian Art. Lund Humphries, 1972. Standard reference for the mandorla in Christian art.

Definition

Vesica Piscis — Latin for "bladder of the fish" — the lens-shaped region formed by the intersection of two circles of equal radius, each passing through the other's centre. The lens has height equal to the radius and width equal to √3 times the radius (≈ 1.732 r).

The Vesica is the foundational primitive of sacred geometry: it generates the Flower of Life (by stepping along a hexagonal lattice), the equilateral triangle (by connecting the two circle centres and either lens-vertex), and the canonical Romanesque-arch profile (by inverting the lens).

Etymology and origin

The figure appears in Euclid's Elements, Book I Proposition 1 — Euclid uses two intersecting circles to construct an equilateral triangle, and the lens between them is implicit. The term Vesica Piscis entered Christian iconography in the early Middle Ages as the mandorla ("almond"), the aureole surrounding depictions of Christ in Majesty (the Vatican's Romanesque tympana, Chartres Cathedral, etc.).

In Renaissance architecture, the Vesica was the proportion-generator for Romanesque arches, Byzantine domes, and Islamic mihrab niches. The √3:1 ratio of width-to-height appears across all three traditions as the canonical sacred-architecture proportion.

In practice

Use the Vesica overlay when constructing any sacred-architecture facade, Romanesque arch, or Byzantine niche — the lens shape and the equilateral triangle inscribed inside it set the proportions. For modern logo design, the Vesica is the foundation for any "two interlocking circles" mark (MasterCard, Audi, Olympic rings derivations). Interactive overlay: /grids/sacred-geometry/vesica-piscis/.

Sources

Euclid. Elements, Book I Proposition 1 (c. 300 BCE).

Critchlow, Keith. Order in Space. Thames & Hudson, 1969. The Vesica's role in lattice-based geometric systems.

Hourihane, Colum (ed.). The Grove Encyclopedia of Medieval Art and Architecture. Oxford University Press, 2012. Mandorla / Vesica iconography.