Does another Euclidean plane exist other than the parasphere?

[1] Bolyai János, Appendix, North-Holland Mathematics Studies138 (1987) Ferenc Kárteszi (ed), 80., http://dide.ker.sch.gr/emekerkyra/books/Bolyai,J%20Theory%20of%20Space.pdfSearch in Google Scholar

[2] Miroslava Antic, The equidistant involution of the hyperbolic plane and two models of the Euclidean plane geometry, Journal of GeometryVol. 04, Issue 2, (2013), 201–21210.1007/s00022-013-0161-7Search in Google Scholar

[3] Győrfy Zoltán, Az egyenes vonal természetéről – Saccheri és az elpaccolt Mennyország (On the nature of the straight line – Saccheri and the missed Heaven), Ponticulus Hungaricus, XVI. évf. 5. (2012), http://members.iif.hu/visontay/ponticulus/rovatok/limes/gyorfi-saccheri.htmlSearch in Google Scholar