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Carved into the sandstone cliffs of Afghanistan's Bamiyan Valley, the Western Buddha stood 55 meters tall and the Eastern Buddha 38 meters. Their robes were modeled in mud, straw, and stucco over wooden pegs, the upper faces were likely wooden masks, and the larger figure was painted carmine red. Carbon dating of organic material exposed after 2001 dates the Eastern Buddha to 544 to 595 CE and the Western to 591 to 644 CE, when the valley was a wealthy Silk Road oasis ruled by the Hephthalites, or White Huns. The Chinese pilgrim Xuanzang visited in April 630 CE and described thousands of monks, statues decorated with gold and jewels, and a reclining Buddha over a thousand feet long that has never been found.

The Taliban took Bamiyan in September 1998. A commander named Abdul Wahid began drilling into the statues' heads, but Mullah Omar ordered them preserved in July 1999, then in early 2001 ordered all statues depicting humans destroyed, despite protests from the Organisation of the Islamic Conference, Saudi Arabia, the UAE, Pakistan, and offers from India and Japan. Artillery, anti-tank mines, and explosives lowered by rope took almost a month. The blasts exposed 50 unknown caves, and in 2004 synchrotron analysis at the ESRF in Grenoble found walnut or poppy drying oils in mid 7th century murals, the oldest known oil paintings, predating Jan van Eyck by roughly six centuries.

• A ceiling mural pairing a Mithra-like sun god in a golden chariot with winged attendants in Corinthian helmets
• How the statues survived Genghis Khan's forces in 1221 and Aurangzeb's artillery in the 17th century
• Mullah Omar's 2004 claim that he acted in anger over foreign restoration money during drought and sanctions
• UNESCO halting an ICOMOS team's rebuilding of the smaller Buddha's feet with iron rods, bricks, and concrete
• A Chinese couple's 2015 projection of a 180 foot 3D image into the empty niche

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William Beckford inherited a fortune in 1771 at about age ten, with an income estimated at 100,000 pounds a year from sugar plantations in Jamaica, and newspapers called him the richest commoner in England. In 1784 the first Baron Loughborough publicly accused him of an improper relationship with a boy named William Courtenay. The allegations were never proven in court, but society shut him out. He left for Europe with his wife, Lady Margaret Gordon, who died in childbirth in Switzerland, and wandered through France, Germany, Italy, Spain, and Portugal before returning to his family's Fonthill estate in Wiltshire. There he built a six mile wall high enough to stop local hunters from chasing foxes and hares across his land.

In 1796 he hired architect James Wyatt, known for drinking and disappearing, to build a Gothic abbey aimed at Edmund Burke's idea of the sublime. Beckford took charge himself, ran 500 laborers in day and night shifts, and lured 450 more from royal works at Windsor Castle with extra ale. The 300 foot central tower collapsed, was rebuilt over six years, collapsed again, and was ordered rebuilt a third time. Finished around 1813, the abbey had 35 foot doors, yet Beckford used a single bedroom and dined alone on meals cooked for twelve. After losing two Jamaican plantations in a legal dispute in 1822, he sold Fonthill to arms dealer John Farquhar for 330,000 pounds. The tower fell for good in 1825.

• Why his wealth could not buy back a place among the peers who had shunned him
• The 1800 Christmas dinner for Horatio Nelson, cooked in a rushed kitchen that collapsed soon after
• William Hazlitt's verdict that Fonthill was an oversized toy shop and a worthless museum
• Compo cement, timber coated in stucco to look like stone, as the reason the tower kept failing
• Demolition by 1845 and the abbey's stones reused in houses in the village of Tisbury

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At 829.8 meters, the Burj Khalifa is tall enough that residents above the 150th floor break their Ramadan fast about three minutes after those at street level, because they can still see the sun. Dubai under Sheikh Mohammed bin Rashid Al Maktoum built it as a global billboard for diversifying away from oil, and a brief first inspired by Seoul's Tower Palace 3 grew into the anchor of the two square kilometer Downtown Dubai. Ground broke in 2004, and the 2008 financial crisis hit a city carrying at least 80 billion dollars in debt. Abu Dhabi and the UAE federal government stepped in, and at the January 2010 opening the tower long marketed as Burj Dubai was renamed for Abu Dhabi's ruler, Sheikh Khalifa bin Zayed Al Nahyan. Ten months later prices had fallen 40 percent, with 825 of 900 apartments empty.

Skidmore, Owings & Merrill and structural engineer Bill Baker used Fazlur Rahman Khan's bundled tube idea in a Y-shaped plan inspired by the Hymenocallis flower, with 27 spiraling setbacks echoing the minaret at Samarra to break up vortex shedding. The top still sways about 1.5 meters. The foundation rests on 192 friction piles over 50 meters deep, protected from corrosive groundwater by a cathodic system, and concrete was poured only at night and mixed with ice to control curing heat. Behind the Armani hotel and the Atmosphere restaurant on floor 122 was a migrant workforce under the kafala system, which the BBC and Human Rights Watch documented with low wages and confiscated passports.

• How three wings brace one another against wind and twisting forces
• A new high pressure Putzmeister pump built to push concrete about 600 meters up
• More than 35,000 tons of steel salvaged from East Germany's demolished Palace of the Republic
• 36 workers needing three to four months to clean more than 24,000 windows once, with ropes at the spire
• 244 meters of unoccupied vanity height that would rank as Europe's 11th tallest skyscraper on its own

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The first geodesic dome was not Buckminster Fuller's. Walther Bauersfeld, chief engineer at Carl Zeiss in Jena, Germany, built a lightweight triangulated dome on the factory roof after World War I to house a new planetarium projector, and a larger public version opened in July 1926 as the Wonder of Jena. Fuller, working with artist Kenneth Snelson in the late 1940s, coined the term geodesic, secured a US patent in 1954, and pitched the dome as mass-produced housing for everyone. The US Marines began testing domes in 1954: untrained Marines assembled a 30 foot magnesium dome in 135 minutes, a helicopter flew one around at 50 knots, and an anchored dome survived a full day of 120 mph propeller blast. In 1956, 21 domes went up in Canada for the Distant Early Warning Line.

For years the chord factors needed to cut the struts were closely held under Fuller's licensing, until Lloyd Kahn published the tables in Dome Book One and Dome Book Two in the early 1970s and set off a DIY and counterculture building wave. Kahn later turned against dome homes, calling them smart but not wise. Rectangular plywood created waste, custom windows cost 5 to 15 times more, fire escapes and wiring were difficult, furniture fit badly, sound carried across the curved ceiling, and the many seams leaked. Domes instead found their place in big spans and harsh sites.

• Why rigid triangles spread loads across the whole shell, and why a sphere encloses the most volume for the least surface
• Hugh Kenner's account of chord factors guarded almost like classified information
• Designer J. Baldwin's claim that a well-built dome will never leak, versus the wet reality for DIY builders
• Spaceship Earth at Epcot, named after Fuller's own phrase, and the 210 meter Jeddah Superdome
• EcoCamp Patagonia, which opened in 2001 using domes inspired by Kawésqar dwellings, and today's 3D printed seamless domes

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No building in Yangon may rise above 127 meters above sea level, a limit set in deference to the Shwedagon Pagoda. The solid brick stupa sits on Singuttara Hill, about 51 meters up, and rises another 112 meters, covered in gold plates attached with rivets and topped by an umbrella crown set with 5,448 diamonds, 2,317 rubies, and a single 76 carat diamond at the tip. Legend says the merchant brothers Tapussa and Bhallika received eight hairs from the Buddha and brought them to King Okkalapa, who enshrined them with relics of three earlier Buddhas, including a water filter. The royal chronicles first mention the pagoda in 1362 or 1363, when King Binnya U raised it to 18 meters, and later rulers encased each older stupa inside a larger one.

Queen Shin Sawbu raised it to 40 meters and began the gilding tradition, and after a 1768 earthquake toppled its upper half, King Hsinbyushin rebuilt it to 99 meters. Invaders targeted it: Portuguese adventurer Filipe de Brito tried to haul off the 300 ton Dhammazedi Bell in 1608 and sank it in the Bago River, and British troops garrisoned the pagoda in 1824 and again from 1852 for 77 years. Colonial soldiers wearing boots on the terraces sparked the shoe question, which fed Burmese nationalism, and the pagoda became the stage for Aung San in 1946, Aung San Suu Kyi in 1988, and the monk-led protests of September 2007.

• Burmese astrology's eight-day week, with Wednesday split at 6 p.m. and the evening assigned to Rahu
• Eight planetary posts around the base, each with a guardian animal, where devotees pour water on their birth-day shrine
• British engineers tunneling into the stupa in 1824 to test it as a gunpowder magazine
• The 23 ton Singu Min Bell, dropped in the river by the British and floated back up by divers tying on bamboo poles
• Replicas including the Uppatasanti Pagoda in Naypyidaw, built 30 centimeters shorter out of respect, and a 2019 monastery in Chisago City, Minnesota

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Proposals to cross Sydney Harbour began in 1814, when convict architect Francis Greenway pitched a bridge to Governor Lachlan Macquarie, and continued through a floating bridge idea in 1840 and design competitions in 1900 and 1902. Norman Selfe's winning cantilever design was scrapped after a change of government in 1904. Chief engineer John Bradfield revived the project after World War I, with his confidential secretary Kathleen M. Butler running international correspondence and later setting up the project office in London at Dorman Long, the English firm awarded the contract in 1924. The steel arch, modeled heavily on New York's Hell Gate Bridge, was detailed by Dorman Long's engineers Ralph Freeman and Georges Imbault, and a public feud over credit ended with a brass plaque bolted to one of the granite columns.

Workers began the arch in late 1928, driving six million rivets by hand, and 16 men died during construction. The bridge became known as the iron lung for keeping thousands employed through the Depression. On March 19, 1932, as Premier Jack Lang prepared to cut the ribbon, Francis de Groot of the New Guard rode in on horseback in military uniform and slashed it with a sword, declaring the bridge open in the name of the king. The ribbon was retied and Lang cut it with the golden scissors used for New York's Bayonne Bridge in 1931, before a crowd estimated at 300,000 to 1 million.

• Why the four granite-faced pylons carry no load and were built only to reassure the public
• About 250 stonemasons who relocated to Moruya to quarry 18,000 cubic meters of granite for them
• Red-hot rivets tossed to a catcher with a bucket, then shrinking as they cooled to clamp the steel plates together
• Two clergymen who accidentally rode a load-testing train across the day before the opening
• The Bradfield Highway's status as a travelling stock route, the grit-blasting robots Rosie and Sandy, and the Aboriginal flag raised permanently in 2022

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The Atomium is a 102 meter structure on the Heysel Plateau in Laeken, Brussels, built as the centerpiece of Expo 58. Engineer André Waterkeyn and architects André and Jean Polak modeled it on a single unit cell of an alpha iron crystal, a body-centered cubic lattice with nine atoms, magnified 165 billion times. Foundations went in during March 1956 and the structure was finished less than a month before the fair opened on April 17, 1958, with 20 connecting tubes holding escalators up to 35 meters long and a Schlieren lift that carried 22 people to the top in 23 seconds. Wind tunnel tests showed that the original design, balanced on its bottom sphere alone, would overturn in an 80 km/h wind, so bipods were added under the three lower spheres.

Meant to last six months, it was never taken down, and by the 2000s decades of neglect had left it badly deteriorated. A 26 million euro renovation from 2004 to 2006 swapped the aluminium skin for stainless steel, making the iron crystal more chemically accurate than it was in 1958. The stranger fight was legal. Sabam, the Belgian copyright collection society, claimed worldwide rights over images of the building, forced a US website to remove its photos in 2003, and drew a protest in 2008 when organizers in Mechelen had the Atomium erased from public snapshots. Belgium passed freedom of panorama into law in June 2016.

• Why the name joins "atom" and "aluminium" even though the shape represents iron
• The three upper outer spheres, closed to the public because nothing supports them from below
• Old aluminium cladding cut into two meter triangles and sold as souvenirs for 1,000 euros each
• The website that replaced every Atomium photo with a warning that the copyright society would sue
• A children's sphere where school groups aged 6 to 12 can spend the night inside the monument

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New Kingdom pharaohs abandoned the pyramid and hid their tombs in a remote wadi on the west bank of the Nile, beneath the peak of al-Qurn, a mountain shaped naturally like a pyramid. The valley's layers of limestone, marl, and shale made it a treacherous place to dig: when rain reached the shale it swelled and sheared the rock apart, and Setnakht's crews tunneled into an older tomb by accident. The workers who carved these tombs lived at Deir el-Medina, where state records tracked their tools, sick days, and disputes, and around 1159 BC, under Ramesses III, they staged what may be the first recorded labor strike when their grain rations stopped.

Security failed anyway. Papyrus Mayer B, from around 1118 BC, records the confession of a thief named Nesamun who spent four days inside the tomb of Ramesses VI and argued with his crew over bronze bowls and a cauldron. As the state collapsed under Ramesses XI, officials joined the looting, and 21st dynasty priests of Amun secretly moved royal mummies, stripped their gold, and hid them in caches such as the one at Deir el-Bahari. Centuries of flood debris buried the lower entrances, which is why Giovanni Belzoni and Theodore Davis both declared the valley exhausted, and why Howard Carter could still find Tutankhamun in 1922.

• How flash floods raised the valley floor by up to five meters and sealed tomb doors under cement-like scree
• The shift from bent-axis tombs like Thutmose IV's to the straight corridors of Ramesses III and IX, and the well shafts that turned from flood barriers into magical ones
• The Amduat, the Book of Gates, and the Book of Caverns as step-by-step guides through the twelve hours of night
• Why spoil dumped while cutting the tomb of Ramesses VI hid Tutankhamun's entrance from ancient robbers and modern explorers alike
• Ground-penetrating radar from the Amarna Royal Tombs Project, and the discoveries of KV63 in 2005 and KV64 in 2011

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Around 2600 BC, the Fourth Dynasty pharaoh Sneferu set out at Dahshur to replace the stepped pyramids of rulers like Djoser with a true smooth-sided pyramid, reflecting a shift toward the solar cult and the benben mound of creation. His builders began with a 157 meter base and a slope of 58 to 60 degrees, then widened the base to 188 meters and dropped to 54 degrees with inward-leaning layers. At about 49 meters they switched to 43 degrees and horizontal courses, creating the famous bend and a final height of about 105 meters. Physicist Kurt Mendelssohn argued in 1974 that builders panicked after the collapse at Meidum, citing cracked blocks and cedar beams inside. Researcher Tom Lyerman instead argues the steep top ran out of working space for ramps and sleds.

The Bent Pyramid keeps much of its white limestone casing. Engineer Peter James suggests looser joints acted as expansion gaps against desert heat, and NMR studies suggest the casing may be an early cast material bound with diatomaceous earth from the Faiyum. Inside, two separate entrances lead to corbelled chambers over 17 meters high, sealed by portcullises that slid down 45 degree ramps. Quarry graffiti names Sneferu, yet no sarcophagus was found. He then built the Red Pyramid at 43 degrees, the first successful true pyramid, laying groundwork for his son Khufu.

• A 79 meter descending passage, closed for over half a century, reopened to tourists in 2019
• A 4,600 year old cedar beam still props up one portcullis block as part of the locking system
• A satellite pyramid 55 meters south has corridors that resemble a draft of Khufu's Grand Gallery
• Workers leveled the plateau by flooding a grid of trenches and cutting the bedrock to the water line
• Nicole Alexanian and Felix Arnold describe a 700 meter causeway, a wind-deflecting valley temple, and garden basins as a man-made setting built around an artificial mountain

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In 1996 Southwark Council and RIBA Competitions sought a new pedestrian crossing over the Thames, and a team of Arup, Foster and Partners, and sculptor Anthony Caro won with a blade of light. Linking Bankside to the City of London, the bridge frames the south facade of St. Paul's Cathedral, so tall suspension towers were ruled out. Instead the cables run below the deck, pulled taut with 2,000 tons of force across a 325 meter span. The project skipped an Act of Parliament, relying on local permissions, and cost 18.2 million pounds, 2.2 million over budget. It opened a month late on June 10, 2000, when some 90,000 people crossed, up to 2,000 at a time.

The deck lurched sideways up to 70 millimeters, and limiting crowds did not help, so it closed on June 12. The cause was synchronous lateral excitation: walkers widened their steps to keep balance, falling into step with the sway and amplifying it. Engineers tested people on moving platforms at the University of Southampton and Imperial College London and put up to 275 volunteers on the bridge. Rather than stiffen it, they spent five million pounds installing 37 viscous fluid dampers and 52 tuned mass dampers, and it reopened on February 22, 2002. Londoners still call it the Wobbly Bridge.

• Since 1873 a sign on the Albert Bridge has told marching soldiers to break step
• Earlier lateral sway had been recorded on Auckland Harbour Bridge in 1975 and at Birmingham's National Exhibition Centre
• The Millennium Inclinator on the steep Peter's Hill approach broke down so often it was replaced before the 2012 Olympics and later removed in 2021
• Bill Fontana's 2006 Harmonic Bridge piece played the bridge's amplified vibrations in the Tate Modern's Turbine Hall
• Death Eaters destroy it in Harry Potter and the Half-Blood Prince, though the story is set in 1996 before it was built