Officially, it is called the State of Illinois Center, a glutinous moniker conjuring up musty cubicles of clerks in green eyeshades, harried taxpayers with threadbare pocketbooks and endless lines for auto licenses -- the kind of facility universally familiar, something along the daring lines of, say, the FBI Building.

In fact, the State of Illinois Center is one of the wildest and craziest new buildings this side of Katmandu. It banishes forever the notion of state government as a staid, penny-pinching old maid.

Architecture critics are likely to have plenty to say, pro and con, when the building is formally presented to a breathless populace in May.

Whatever the verdict, the State of Illinois Center is the best example of high tack around.

This edifice for the conduct of the people's business looks from the front like an inverted, 17-story teacup made in alternating vertical stripes of clear and mirrored glass, topped with a rakish glass cap. It is surrounded by free-standing pink and gray granite slabs.

Viewed from the back, the "teacup" has been chopped off flush with the edges of the block where the Center sits at Randolph and Clark streets on the north end of the Loop. The square sides, devoid of features except for the stripes, seem to belong to a different building.

Inside, the reason for this shape becomes, well, less incomprehensible. Under the south-facing teacup is a stupendous atrium, held up by a breathtaking latticework of red steel trusses. It arches the full height of the Center, higher even than the last 17 Illinois state deficits. Curving balconies open onto the atrium at each floor.

There are visual echoes here of an opera house . . . or a Big House. Glass elevators in two tiers whiz up and down with dizzying speed.

The floor is made from concentric gray marble slabs divided by black marble swaths inlaid with white dots that accentuate the curved interior. On the lower level, where state buildings sometimes have basement vaults to store tax money, there is a sunken circular floor in black and white marble. From the balcony outside the governor's offices on the 16th floor, the sunken circle looks like nothing so much as a bull's-eye.

But Gov. James R. Thompson (R), who chose the design from three offered by avant-garde Chicago architect Helmut Jahn, loves the adventure-as-building.

"You have moved into what is perhaps the most innovative and exciting public building in the United States," he writes in a welcome letter to state workers arriving from a dingy, 60-year-old rabbit warren across the street.

Thompson happily moved in last November. His suite includes a small office, kitchenette, bathroom, sitting room and private elevator that carries him from the office to his private parking space in the garage deep beneath the bull's-eye.

Cost overruns have driven the price for the 1.2 million-square-foot building to $172 million. Thompson calls it a bargain. But there are rumbles of a legislative probe. In traditional Chicago style, this may get rolling in time for the 1987 election, when Thompson is expected to seek a fourth consecutive term.

City fire officials have raised serious questions about the building's fire safety, but the state continues to occupy it and the formal dedication is scheduled for next month.

For startled bureaucrats gingerly moving their out-baskets into position throughout the upper floors, it has been something less than love at first sight.

Each floor is laid out in a ring of offices that opens onto the atrium balconies. The proximity of what one employe calls "the void" beyond the balcony has proved unnerving to many.

This may change when the building is fully occupied; the first three floors are to contain shops and restaurants, and the bustle of mall-like activity below is expected to calm workers high above.

The building's odd shape has altered the maze of offices within each ring: Some are square, some rectangular, some combinations of square and curved. Some have narrow, pie-shaped corners, some have walls in no particular shape. Depending upon one's sense of direction, this can be exhilarating or merely confusing.

All such complaints pale in the face of one big gripe: Many offices don't have doors. Even in a state where strong sunshine laws can make shutting one a civic sin, bureaucrats don't like to do without doors.

"Very few people can have doors," groused a new arrival to a friend as they strolled around her mostly doorless domain recently. "It's one of the cost savings. Only very important people get doors. It's going to take a while to get used to.