"Maybe this is a b.u.m lead -- but I think I know why we're repeating worlds. And maybe how to snap out of the loop in controlled fashion."

She sat effortlessly, the muscles in her stomach tightening. "Speak."

He showed her his plastic construct, opaque because of its many layers. "You know what this is?"

"A doodle from plane-frame material."

"A hexa-hexaflexagon. See, I flex it like this and turn up new faces."

She took it and flexed it. "Clever. But to what point?"

"Well, they don't come up in order -- not exactly. Look at the face numbers as you go -- and at the composition of the repeats."

"One," she called off. She flexed. "Three... Two... One... Five... Two, inverted." She looked up. "It's a double triad. Intriguing, not remarkable."

"Suppose we numbered the worlds we've been going through -- and found a repeat that was backwards? I mean, the same, but like a mirror image?"

For the first time, he saw an agent do a double take. "The second blizzard was backwards!" she exclaimed. "Or rather, twisted sixty degrees. The igloo -- the irregularities in it and pattern of our prior tracks, what was left of them, the projector -- all rotated by a third!"

"Yeah. That's what I figured. Didn't make sense at first."

"Flexing alternates! Could be." Rapidly she flexed through the entire sequence, fixing the pattern in her mind. "It fits. We could be in a six-face scheme on this framework. In that case our next world will be -- the forest." She certainly caught on rapidly! "But we can't go home from there."

"No. The face will be twisted, part of a subtriad. But we would know our route."

"Yeah," he agreed, pleased.

She pondered momentarily. "There's no reason the alternates should match the hex faces. But there is a clear parallelism, and it may be a useful intellectual tool, in much the way mathematics is a tool for comprehending physical relations. Our problem is to determine the validity of our interpretation without subjecting ourselves to undue risk."

"You sound like Cal now!"

"No shame in that," she muttered. "Your friend has a freakishly advanced intellect. We could travel the loop again just to make sure -- but that would mean a delay of several hours, waiting for the projectors to recharge. In that time our compet.i.tion could gain the advantage."

"So we just go ahead fast," Veg finished. "We can follow the flex route and see if it works. If it does, we've got our map of alternity."

"In your b.u.mbling male-normal fashion, you may have helped me," Tamme said. "Come here." Veg knelt down beside her.

She put both hands to his head, pulled him to her, and kissed him. It was like the moment in free fall when a s.p.a.ceship halted acceleration in order to change orientation. His whole body seemed to float, while his own pulse pounded in his ears.

She let him go. It took him a moment to regain composure. "That isn't the way you kissed me before."

"That was demonstration. This was feeling."

"You do feel? I thought -- "

"We do feel. But our emotions are seldom aroused by normals other than amus.e.m.e.nt or distaste."

Veg realized that he had been paid an extraordinary compliment. But that was all it was. He had helped her, and she was appreciative. She had repaid him with a professionally executed gesture. Case dismissed.

"We should have a choice here," she said. "Repeat the triad indefinitely -- or break out of it. Only way to break out is to project elsewhere than to the plane world. But how can we do that -- without interfering with the settings on the projector?"

Veg appreciated the problem. Touch those settings, and they could be thrown right out of this hex framework and be totally lost -- or dead. That would accomplish nothing worthwhile. They wanted to follow the existing paths wherever they led, and catch up to -- whom?

"These settings are built into the hexaflexagon," he said. "All you have to do is find them."

"Yes. Too bad alternity isn't made of folded plastic."

They remained in silence for a time, while the music swelled around them. And Veg had a second revelation. "The music!"

Again she caught on almost as fast as he thought of it and quickly outdistanced his own reasoning. "In phase with the music! Of course. Catch it during one type of pa.s.sage, go on to Plane. Catch it during another -- "

"Now's the time!" Veg cried.

They ran to the projector. Tamme had it on instantly.

And they were in the forest.

"Victory!" Veg exclaimed happily. Then he looked about uncertainly. "But is it -- ?"

"Yes, it is rotated," Tamme said. "So it is part of a different triad. There'll be another odd-handed projector here."

They located it, and it was. "Hypothesis confirmed," she said. "Now if our interpretation is correct, we won't have to worry about being sent back to Blizzard because this inverted version is part of a different loop. The next one should be new. Brace yourself." She reached for the switch.

"Sure thing," Veg said. "I'm braced for one new world."

It was new, all right. Veg's first impression was of mist. They stood in a tangibly thick fog. He coughed as the stuff clogged his lungs. It wasn't foul, just too solid to breathe.

"Get down," Tamme said.

He dropped to the ground. There was a thin layer of clear atmosphere there, below the fog bank, like air trapped beneath river ice. He put his pursed lips to it and sucked it in.

"Crawl," she said, her voice m.u.f.fled by the fog.

They crawled, shoving aside the fog with their shoulders. Suddenly the ground dipped -- but the bottom of the fog remained constant. It was too stiff to match the exact contour of the land. Now there was squatting clearance beneath, then standing room.

"That's some cloud!" Veg remarked, peering up. The stuff loomed impenetrably, a pall that blacked out all the sky. Wan light diffused through it. "Stuff's d.a.m.n near solid!"

"You liked it better under the pine tree?" Tamme inquired. She was already looking for the next projector.

"Sure did!" He had the nagging feeling the fog bank could fall at any moment, crushingly.

A valley opened out before them. Tamme stared.

Veg followed her gaze. "A fog house?" he asked, amazed.

It was. Blocks of solidified fog had been a.s.sembled into something very like a cabin, complete with slanting, overlapping fog tiles on the roof. Beyond it was a fog wall or fence.