Geodesic
The space of Schwarz–Klein spherical triangles
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020) no. 3, pp. 263-282
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We describe the space of spherical triangles (in the sense of Schwarz and Klein). It is a smooth connected orientable $3$ manifold, homotopy equivalent to the $1$-skeleton of the cubic partition of the closed first octant in $\mathbb{R}^3$. The angles and sides are real analytic functions on this manifold which embed it to $\mathbb{R}^6$. 
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Alexandre Eremenko; Andrei Gabrielov. The space of Schwarz–Klein spherical triangles. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020) no. 3, pp. 263-282. http://geodesic.mathdoc.fr/item/JMAG_2020_16_3_a3/

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