"It figures," he said. "We've used up all the faces."

"In which case we'll be back where we started -- closed loop, and n.o.body but ourselves."

"I guess so, right now. The others must have gotten off. Is that bad?"

"I can't buy it. Who set up all these other projectors?"

Veg shook his head. "Got me there! If they'd gotten off, they'd have taken back their projectors -- so they must be still on. And there can't be six Vegs and six Tammes." He sobered. "Or can there?"

"Suppose your hexaflexagon had twelve faces?"

"Sure. There can be any number of faces if you start with a long enough strip of triangles and fold it right."

"A twelve-face construction would merely add one new face to each of the six exterior angles," she said.

Veg shrugged. "I'll take your word. I'd have to make a live hexaflexagon to check it out myself."

"Don't take my word. Make your construction."

"Here? Now? Why not get to a better alternate to -- "

"No."

"I don't have anything to -- "

She took apart the six-faced hexaflexagon, straightened out the long folded strip of plastic, pried at the edge with a small knife that appeared in her hand, and peeled it into two layers lengthwise. She produced a little vial of clear fluid, applied it to the edges, and glued the strips together endwise. The result was a double-length strip.

Veg sighed. He took it and folded it carefully. He made a flat spiral so that the double length became the size of the original but with two layers instead of one. Then he fashioned a normal hexaflexagon.

"Run through it and number your faces," Tamme said.

"Okay." This was a more complicated process, involving thirty flexes, but in due course he had it. Meanwhile, Tamme had been making a new diagram.

"Now start at face One and flex," she said. "I will call off your numbers in advance. Five."

He flexed. "Five it is."

"Seven."

He flexed again. "Right."

"One."

"Right again. Hey, let me see that diagram!"

She showed it to him. It was an elaborated version of the prior one, with new triangles projecting from each of the six outer points. One angle of each of the outermost triangles carried the number of a new face, bringing the total to twelve.

They flexed through the rest of the construct. It matched the diagram.

"As I make it," Tamme said, "We could be on this one instead of the six-faced one. In that case our starting point would be Seven, followed by One, Five, Two, Eight, Five, Two, One, and now Three. If so, both our next two stops may be new worlds, Six and Nine."

"Instead of repeats!" Veg said. "That's the proof right there. All we need to do is try it. If we don't like the new ones, we just skip on to Three, there in the loop -- that's here. Our map is still good."

"Unless this is actually a mere subsection of an infinitely large configuration," she cautioned. "In that case, it is only a hint of a route through it. But we could probably find our way back, though there is no longer any way to travel back the way we came." She paused, peering at him through the mist. "If something should happen to me, you use this diagram to return to your friends in the City."

"Not without you," he said.

"Touching sentiment. Forget it. Your philosophy is not mine. I will leave you instantly if the need arises."

"Maybe so," Veg said uncomfortably. "So far there hasn't been any real trouble. Maybe there won't be."

"I rate the odds at four to one there will be," she said. "Someone set up these projectors, and in at least one case it was another agent just like me. Of course I'm used to dealing with agents just like me -- but they have been Tara, Tania, and Taphe, not alternate Tamme's. I mean to find that other agent and kill her. That will be difficult."

"Yeah. Different philosophies," Veg said. He knew she read the disapproval in him. Maybe it would be better to leave her if it came to that.

"Precisely," Tamme said. And activated the projector.

They were in a curving hall. Checkerboard tiles were on the floor and a similar but finer pattern on the flat ceiling. The walls were off-white. Light shone down from regularly s.p.a.ced squares in the ceiling pattern. It was comfortably warm, and the air was breathable.

"So you were right," Veg said. "A new alternate, a larger pattern. No telling how many agents in the woodwork."

"It is also possible that these are all settings on the same world," Tamme said. "That would account for the constancy of gravity, climate, and atmosphere."

"That blizzard wasn't constant!"

"Still within the normal temperature range."

"If they're all variations of Earth, that explains the gravity and climate. You said yourself they were different alternates. Trace distinctions in the air, or something."

"Yes. But perhaps I was premature. It could be as easy to regulate the air of a particular locale as to arrange for travel between alternates. Matter transmission from one point on the globe to another would cover it. I merely say that I am not sure we are actually -- " She stopped. "Oh-oh."

Veg looked where she was looking but didn't see anything special. "What's up?"

"The walls are moving. Closing in."

He didn't see any difference but trusted her perception. He was not claustrophobic, but the notion made him nervous. "A mousetrap?"

"Maybe. We'd better locate that projector."

"There's only two ways to go. Why don't I go down here, and you go there? One of us is bound to find it."

"Yes," she said. There was a slight edge to her voice, as if she were nervous. That was odd because agents had excellent control. They were seldom if ever nervous, and if they were, they didn't show it.

"Okay." He walked one way, and she went the other. But it nagged him: What was bothering her so much that even he could notice it?"

"Nothing," he muttered to himself. "If I pick it up, it's because she wants me to." But what was she trying to tell him?

He turned about to look back toward her. And stood transfixed.