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Martin Sleziak
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There has been workwork on Gram matricesGram matrices that appears relevant, see e.g. Theorems 14-5 on p. 24-5.

Also of peripheral interest: there is a hyperbolic generalizationhyperbolic generalization of the Dehn invariantDehn invariant. But as far as I can tell this sort of thing can't really be a generalization of any 2D construction.

There has been work on Gram matrices that appears relevant, see e.g. Theorems 14-5 on p. 24-5.

Also of peripheral interest: there is a hyperbolic generalization of the Dehn invariant. But as far as I can tell this sort of thing can't really be a generalization of any 2D construction.

There has been work on Gram matrices that appears relevant, see e.g. Theorems 14-5 on p. 24-5.

Also of peripheral interest: there is a hyperbolic generalization of the Dehn invariant. But as far as I can tell this sort of thing can't really be a generalization of any 2D construction.

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Steve Huntsman
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There has been work on Gram matrices that appears relevant, see e.g. Theorems 14-5 on p. 24-5.

Also of peripheral interest: there is a hyperbolic generalization of the Dehn invariant. But as far as I can tell this sort of thing can't really be a generalization of any 2D construction.