"Share in our celebration of victory," another said. "The reflectives never suspected the richness of our symmetry until it was thrust upon them-no less than fourteen, and now they have been expulsed from every one. They did not have a chance for an exchange of bodies, not a one."

"From which did you come?" a third asked. "One of the lesser triangles of the central pentagram, or perhaps an octagonal node from the hypersphere of the great triad?"

Kestrel opened his mouth to speak but Astron was quicker. "What is the map?" the demon asked. "The lines in red and the nodes in blue with the crossed-out annotations-what do they mean?"

"It is the rendering of the great polytope, all that there is," answered the first. "See, already we make the changes that mark the victory." The warrior stopped and jabbed rapidly at the parchment. "It is all in accordance with the second protocol-all moves are simultaneous. We have occupied nodes here and here and then those over on the other side. They form the vertices of a figure with more than thirty edges. The reflectives were too concerned about this minor symmetry of three adjacent nodes here to notice what we had done.

"Look at the pattern closely, see how all thirty-seven form a beautiful pattern that is invariant if it is rotated

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through the small angle drawn over there." The warrior's face widened in a satisfied grin. "As the first protocol states-the greater the symmetry the greater the power. In perfect synchronization, those of us occupying the first node of the set began the journey to the second; those at the second unto the third. The reflectives who occupied part of the pattern were totally unprepared and the pressure to preserve symmetry was too much to resist. They were dragged from their fortifications into other nodes where yet more of us waited. We have won possession of more than a dozen."

Kestrel looked at the map where two of the warriors were busy erasing some sort of symbol by some of the nodes and replacing it with another. He glanced at Astron in confusion, but then relaxed when he saw that the demon had not wrinkled his nose.

"This map then is a reproduction of all that we see." Astron waved his arm outward toward the desert. "These oases are the nodes and the lattice lines the paths between them."

"It is a record of all the realm," added one of the warriors.

"And the symbol you are erasing-the nodes that are marked with it are under the control of the ones you call the reflectives." Astron stopped and studied the parchment for a moment. "You hold your territory most unlike the fashion of the realm of men," he said. "Look at how interspersed you are. How can you possibly say who has the greater advantage?"

"It is not a matter of adjacency, but of symmetry. Look at the beauty of the nodes that we possess. Of very high order are the subgroups that describe our lands."

"And that symmetry gives us power, power to strike at a dozen vertices as one, power to use the innate forces of the realm to aid us rather than fight against it in furthering of our aims."

"But why fight at all?" Astron asked. "What motivates you against these you call the reflectives?"

"Their symmetries are most foul," the first of the warriors spat. "They are invariant under reflection

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whereas ours remain the same when subjected to rotations instead. And as the fifth protocol states-victory is total, only one of two will be left. It is the duty of every rotator to resist reflectives wherever we can, to strive to eliminate them until none are left to poison the beauty of the true symmetries that we will build when they are gone."

"1 don't understand any of this," Kestrel said. "It must be some sort of threadbare dream-scattered oases in a vast desert linked by geometrical designs, warriors engaged in mathematically obtuse campaigns. What of women and the crops that supplement these few fruits? Who weaves the clothes you wear on your backs and from where do the woolens come?"

"Most of your words make no sense whatsoever,",the first warrior said. "Our lives are to fight the reflectives until either we receive mortal wounds or have totally won. The fruit of the trees provide us subsistence; our armor protects us from blows. Of these other things we have no need."

"But replacements," Kestrel persisted. "What happens when some of your number are indeed struck down?"

"Replacement?" the warrior echoed. "I do not comprehend. We fight the reflectives until one of us is victor. If some of my comrades fall, we recompute the symmetries for the numbers remaining, so that we have freedom of movement about the subnodes, as you see we have done here. There are no replacements. There never have been since the beginning of time."

Kestrel looked quickly about the oasis and noted that the warriors were deployed in what appeared to be a random fashion onJy at first glance. Closer examination revealed that the subgroups by each tree were different in many distinct ways from all the rest. Each had a different number, and the heights and weights were well distributed as well. The camp tasks they had undertaken were all unique and the identical weapons were stacked only where other differences outnumbered the similarities.

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Kestrel glanced at Phoebe's almost vacant stare and Nimbia's listless sh.e.l.l hunched next to her. He looked back out onto the featureless desert. All that he could see was no more than the creation of one of the fey, he realized. It all had come into existence only by the force of thought-just like a scribe transcribing flights of fancy for the sagas, leaving out all nonessential detail. One could not really expect any more.

And they were marooned! The words boomed through his mind. Marooned in a universe in which all life apparently had to offer were the few simple rules of a game.

CHAPTER EIGHTEEN

Artifacts of the Chronoids.

KESTREL looked across the new oasis at Phoebe and forced his face into a smile. He had lost track of the number of nodes to which they had been transported, but it would do her spirits no good to show how low his own had sunk. Far better it would be as well if they could share the same subnode, but the rotators, with their rigorously balanced deployments, insisted that they be kept apart.

Nimbia on occasion seemed a little more alert, but most of the time she still dozed in her stupor at the base of the tree to the right of Phoebe's. Although Astron was at Kestrel's side, the demon again was occupied with learning about some obscure detail of the realm. Kestrel was alone with his thoughts.

More than he feared, the life of a rotator was one of almost complete ritual. In a rigid sequence they would plan, eat, sleep, and then, simultaneously with everyone else in the realm, rush over the sands to a new node that

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looked almost exactly the same as the one they had left behind. Then, if the new node were unoccupied and there were no battle, the cycle would begin again. Plan, eat, sleep, move-they were merely playing pieces on a complex board, jockeying for position without ceasing.

Kestrel looked at the six fruit-bearing trees that ringed the small pond of water and then out over the featureless desert, trying to channel his thought in a more productive direction. He kicked at the sand at his feet, barely missing another shaft of ornately carved metal.

"Abel, what are these things?" he called out to the commander of the warriors. "Half of the oases we have visited seem to have them protruding from the ground."

One of the warriors looked up from where he had been conversing quietly with two others over the small portable table covered with the maps of the nodes. His complexion was slate gray like the rest, but streaks of black ran through his hair. His eyes were steady and unblinking in a face not creased by either smile or frown.

"They are the devices of the chronoids," Abel said with disgust in his voice, "the machines of beings of another realm-another realm just the same as yours. In our haste, we do not bury them as we might. They are a violation of the protocols."

"Another realm." Astron looked up from the scroll he had been studying intently. "We are not the only visitors you have seen?"

"Indeed not," Abel said. "Ever since the reflectives seized the origin, the visits have been most frequent. The chronoids look much as we do and they engage in some great struggle not so very different from our own. But their weapons are not similar in the least and they are difficult for us to understand."

"What kind of weapons?" Kestrel said, suddenly interested. "Something that would give you an advantage if you had them instead? Do they by chance involve the use of fire?"

"We would not use the devices of the chronoids." Abel pursed his lips. "The reflectives do so only at great

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peril, since they work so imperfectly in a realm different from which they were intended." The commander stopped and looked at Kestrel intently. "More importantly, they are not part of the tradition that stretches back to the memories of our creation. Only the reflectives would think of trying something so base to gain advantage."

"But where are-"

"Perhaps it is worth the effort to show you one of the foul things," Abel said. "Then you might better understand." He gestured to one of the other gray warriors. The second began to protest but Abel's stare cut short the words. The warrior spat at the ground at his feet and then began digging into the sand. Shortly he retrieved an oblong box of metal and brought it forward for the others to see.

"Why, it looks like a clock," Astron exclaimed as the object drew closer. "A device for measuring the pa.s.sage of time. See the three ornate bands of metal pivoted at the center of the circular face with symbols about the rim."

"These devices do much more than merely count the swings of a pendulum," Abel said. "Just as our realm is governed by the symmetries of s.p.a.ce, so is that of the chronoids ruled by the symmetries of time. With these clocks, as you call them, they manipulate the order of events in strange ways.

"Here, in the realm of the reticulates, the devices behave in manners even more bizarre. The manipulations of time are somehow transformed to ones of s.p.a.ce instead. In battles where the reflectives possess them, I have seen entire moves undone against our wills, even though we held the advantage-whole squads of men exchanged with those of our enemy so that we were outnumbered, rather than the other way around."

"How did this clock come to be here?" Kestrel asked,

"Somehow the reflectives have found a way to communicate between the realms, exchanging men with the chronoids for weapons that aid their own cause. Recently the reflectives seem to have increased the fre-

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