Fumihiko Maki creates a minimalist, angular home for the Aga Khan Museum in Toronto

Every monumental museum is inspired by a great collection. In the case of the sparkling white-stone Aga Khan Museum, opening next week in the outskirts of Toronto, it's the 1,000 Muslim texts, architectural elements, fountains, crystal, paintings and shahnameh, or epic poems, amassed by the holy leader of the Ismailis and his ancestors.

When, in 2007, he began a public tour of his private collection, the Aga Khan sought out Fumihiko Maki to fashion its permanent home. A Pritzker Prize-winner from Japan and architect of the Aga Khan Foundation's Canadian headquarters in Ottawa, Maki drew up 10,000 sq m of towering gallery spaces housed within a minimalist angular form - shaped not unlike an open packing box - assembled on a precise grid of 1m Brazilian granite slabs. (He might have used marble had the climate not been so unforgivingly Canadian.)

The angled facades were designed to play with the arc of the sun, throwing light and shadow onto the surrounding terraces and reflecting pools. 'The play of light is the focus,' says Andrew Bernaus of Moriyama & Teshima, architects of record on the project, 'not the design.'

The light effects continue inside, where a small stone courtyard (with a star-shaped drain at the centre and underfloor heating to melt the winter snow) is enclosed in glass etched with a mashrabiya pattern, an ancient Islamic motif reinterpreted by Maki. Light filtered through the patterns splashes on the white walls at different elevations throughout the day. In the upper galleries, built to house the temporary exhibitions, hexagonal skylights, or 'lanterns', introduce shafts of ambient light - the hexagon being symbolic, in the faith, of heaven. Curator Henry Kim, plucked from the Ashmolean Museum in Oxford to run the Aga Khan, says, 'When it's partly cloudy, the natural light raises up the light levels, then the clouds drop it down - so you can see the space breathing.'

Elsewhere the surfaces are flawlessly smooth, from the black granite that conceals the escalators to the slender 10m-high steel columns that anchor the white granite walls. Those walls are soundproofed for acoustics, to foil the high ceilings. Even the exit doors and electrical panels are hidden within the surfaces, invisible to anyone who doesn't know of their existence. Bernaus references Adolf Loos' Ornament and Crime when he says, 'You don't use ornamentation to cover things up just because you can't figure it out.'

In the auditorium, the building's crown jewel, the temperature is controlled from grilles hidden beneath each individual seat. That allows the origami dome, inspired by a bazaar in Iran, to rise unfettered over walls panelled with strips of teak. An angular access staircase spirals around in a hexagonal formation, divine against lapis-blue plaster wall, Maki's only concession to colour.

It's a palette that will please Toronto's Ismaili community, accustomed to the simple, cool aesthetics and vast, naturally lit spaces. Yet Kim, who is collaborating with the Hermitage and Louvre museums on some exhibitions, is adamant his museum offers a secular experience. 'The Muslim population is the "low-hanging fruit", to be sure,' he says, 'but our collection is a primer, for everyone, and part of a trend in Islamic art, which is rising to the surface as a significant artform.'