Futuristic Pyramid

Pyramids. The distinct shape, clean vertices, and inherent coolness have fascinated humanity since the Egyptians. Some sci-fi writers like to stick modern or futuristic-looking pyramids into their works to combine old and new in a distinctive yet recognisable manner. The result is the future pyramid, a building in the style of ancient Egypt but using modern or yet-to-be-invented materials and construction methods. The primary reason for these is that they look impressive.

A pyramid is a good shape for a space-frame building, if you've got enough room for a wide building. But how many of the examples use that as justification?

Examples of Futuristic Pyramid include:

Anime and Manga

Digimon Adventure: A literal Inverted Trope, Etemon's base is an upside-down pyramid, which connects to an underground octahedron (think two pyramids connected at their bases).
The NERV HQ in Neon Genesis Evangelion is a pyramid. There's also a pit shaped like an inverted pyramid located in front of it.
Mega-Tokyo of Bubblegum Crisis. The Genom Tower in particular is more of a cone, but it still has the spirit of this trope.

Card Games

The Yu-Gi-Oh! cards "Level Limit - Area B" and "Level Limit - Area A" both have big pyramids in the background.

Comic Books

Microwave Mountain in Rogue Trooper, originally a giant solar power plant, now a Nort stronghold. Shaped like a pyramid, for no real reason.
In Enki Bilal's La Foire aux Immortels (and the movie Immortal inspired from it), the Egyptian gods live in a pyramid that is also a cool spaceship. And it's going to destroy Paris (New York in the movie) unless they get fuel.
Apocalypse of X-Men is fond of pyramid motifs, which makes sense as he was born in Egypt a few thousand years ago.

Film

Ra's ship in the original Stargate movie.
- And SG-1 extends this to the Goa'uld as a whole: they may be impersonating a Greek, Babylonian or even Japanese deity but the snake will still use pyramid shaped spaceships, space stations, evil lairs...
  - Except for Anubis (or Ba'al in Continuum) , whose flagship is dome-shaped and can alter its configuration to fire its Wave Motion Gun.
  - The original film showed that Ra already had a pyramid ship when he first came to Earth. This indicates that they already had the Ha'tak design before they forced humans to build pyramids to land on them. No explanation as to why all cultures with Goa'uld ties did not have pyramid landing sites.
  - The Pyramid Ships can land on Mountains, so they probably didn't need them elsewhere.
Tyrell Corporation headquarters from Blade Runner.

Literature

The Doctor Who Eighth Doctor Adventures novel Parallel 59 features a futuristic Uncanny Village where a great deal of the buildings are pyramids. Apart from the protagonist, who's from lightyears and centuries away and is constantly reminded of ancient Egypt, everybody is used to them.

[...]the pyramids rising over the skyline. Like a nice clean Egypt. Mystery. Power.
The girl yawns, it makes me smile. The pyramids are here to reassure, not to inspire. To the Homeplaneters, they're mundane, just the way dwellings are built. None of the resonances or associations they have for me are flitting through her mind, I can tell.

In Ramsay Campbell's Cthulhu Mythos stories, the Insects from Shaggai build pyramidal temples to Azathoth that can teleport between planets.
Patrick Tilley's novel Fade-Out. When an alien ship lands on Earth, it starts to grow a gigantic pyramid which eventually shuts down human technology.
The Great (and Lesser) Redoubts in The Night Land, enormous pyramids (the Great is over seven miles high, slightly taller than Everest) of seemingly indestructible metal that are humanity's last home on an Earth that has become a hostile monster-ridden wasteland.
In Lois McMaster Bujold's latest Vorkosigan Saga novel, Cryoburn, one of the largest cryogenic companies on the planet Kibou-daini is NewEgypt. Their cryo-storage facilities (where they keep the frozen bodies of people who were hoping to be revived, when there's a cure for whatever was killing them) are all in pyramid shaped buildings, and all their corporate branding follows an Egyptian theme. (They've trademarked the entire historical era, to block imitators.)

Live Action TV

The original 1970s Battlestar Galactica episode "Lost Planet of the Gods" part 2. The planet Kobol has pyramids, the remains of an ancient civilization.
- Caprica also had pyramidal buildings
  - The reimagined series also had ~~Virgon~~ Gemenon, which had mostly pyramidal buildings.
Chouriki Sentai Ohranger / Power Rangers Zeo: The massive carrier Zord King Pyramidder / Pyramidas. It shoots lightning, transforms into a huge robot, and combines with the rest of the team's mecha.

Music

Some of Gamma Ray's album covers feature Futuristic Pyramids...IN SPACE!

Tabletop Games

Necron monoliths in Warhammer 40,000.
Traveller Classic.
- Double Adventure 1 "Shadows". The PCs must investigate a pyramid to free their spaceship from a death trap.
- Journal of the Traveller's Aid Society #13, adventure "Thought Waves". The PCs are trapped inside an underwater alien pyramid that's actually an ancient spacecraft.

Video Games

The main Protoss building in StarCraft, Nexus, is a pyramid.
Command & Conquer: During Tiberian Sun, NOD was in love with this trope, having their major headquarters within pyramids. By Tiberium Wars, Nod largely went back to their original awesome base, but they did deploy their Epic Unit from a pyramid-shape structure.
Commander Keen 4: Secret of the Oracle has four levels (one of them secret) that take place inside a pyramid. Whether they're new pyramids, or ancient pyramids improved with some modern technology (laser turrets, doors etc.) remains unknown.
Some Prothean remains in Mass Effect.
Star FOX 64's planet Katina has a pyramid as its main and only building. Assault changes it to a futuristic tower but keeps some vaguely pyramidesque aspects.
The Imperial Palace in Starsiege is one of these. Bonus points for being located in what used to be Egypt.
Mental Institution level of Serious Sam II is a large futuristic pyramid on treads and plenty of weapons and reinforcements.
In Unreal Tournament 2003, the Anubans (or Nakhti, as they are called later), who are basically space Egyptians, are fond of these. One of the most prominent Futuristic Pyramids can be found in the map CTF-Face3.
The city of Adrianopolis (and possibly others in the World Union) in Culpa Innata features a gleaming pyramid at the center, which has clubs, restaurants, bars, stores, etc.
Kirby 64 The Crystal Shards: The final stage set on Rock Star is mostly inside a large space station shaped like a pyramid.
The earliest examples are in the 2D shooter Xevious.

Real Life

A very elongated example is the Transamerica Pyramid in San Francisco.
I. M. Pei's glass pyramid at the Louvre was an attempt to invoke this.
The Rock and Roll Hall of Fame and Museum started out as a glass pyramid, and then was expanded upon.
From the point of view of, say, Christopher Wren, the Eiffel Tower would be a good example of this: a tall pointy building made of yet-to-be-discovered materials and construction techniques.
The Luxor casino in Las Vegas also invokes this trope, with a glass pyramid-shaped main building and general Ancient Egypt theme (although David Foster Wallace preferred to compare it to a "ziggurat from Babylon of yore").
Similarly, the Hard Rock Cafe in Myrtle Beach, South Carolina is a pyramid with Egyptian-themed decor but ultramodern design.
The Ryugyong Hotel in North Korea masterfully combines this with Compensating for Something.
The Pyramid Arena in Memphis, Tennessee. Which Memphis did you expect?