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Menu said the sect doesn't keep records on its total membership, but said there were usually around 10 people who attended twice weekly meetings at the pyramid. Since the case went to the Supreme Court, Summum has seen a boost in traffic to its Web site, its main means of disseminating information about the faith, and from which it sells books written by Ra and other items, including "merh," a sex lubricant purportedly made through interpreting ancient Egyptian hieroglyphs.
The pyramid, a 27-foot tall structure covered with copper plate is the faith's headquarters and contains the mummified remains of Corky Ra, born Claude Rex Nowell, who first brought suit against Pleasant Grove City over the monument in 2003 and died in January at 63.
Though Ra is the only person the sect has mummified, Summum has preserved several pets, including Menu's poodle, many of which are displayed in the pyramid.
Menu said thousands of people have contacted Summum for information about being mummified.
At oral arguments last Wednesday, the justices posed a range of hypothetical questions to figure out how free speech should be exercised both by cities and individuals.
"You have a Statute of Liberty. Do we have to have a statue of despotism?" asked Chief Justice John Roberts. "Or do we have to put up any president who wants to be on Mount Rushmore?"
Justice John Paul Stevens asked whether calling something "government speech" meant a monument could be rejected simply because you dislike its message.
The court has yet to pass down a single sweeping ruling that applies to all religious monuments in public spaces. In 1980, displays of the Ten Commandments were banned from public schools. In 2005, the court allowed a 57-year-old Ten Commandments monument to remain on the grounds of the Texas statehouse but that same year ordered the removal of a the Decalogue from the walls of two Tennessee county courthouses.
The Summum case asks the Court to draw a distinct line on religious monuments in public spaces, which it has been reluctant to do in the past.
"There is a fundamental difference between opening up a forum, taking acres of a park and saying everybody gets to go in," said Jay Sekulow, head of the American Center for Law and Justice, which is representing the city, "and another situation where the government is clearly controlling it not for a subversive reason."
Sekulow told ABC News.com that Summum's beliefs "did not factor into the city's decision to not grant a permit for the monument. They didn't know anything about Summum. They didn't know about the Seven Aphorisms. They just knew that monument had nothing to do with the history of the park."
The Court is not expected to reach a decision until the spring, but Menu said either way they'll continue to fight for the right to free speech and free exercise of religion.
In the pyramid, adherents also brew an alcoholic beverage they call "nectar," or "liquid knowledge," consumed before meditation sessions.
Menu said she knows some of the religion's practices may seem strange, but that all religions do things that seem weird to outsiders.
"We're always being slammed with the label 'New Age,' and being called a 'New Age group.' What does that even mean?" Menu said. "We're not weirdos worshiping mummies, like some people have suggested. We're normal people trying to understand the universe and taking a spiritual journey."
As for the aliens who visited Ra in the 1970s, Menu said many religions believe in similar visitations.