Pyramid 301
Preview $$U_{301}(x, y) = \frac{2 \sin{\left(\frac{\arcsin{\left(\sqrt{\frac{27 x}{4} + \frac{27 y}{4}} \right)}}{3} \right)}}{\sqrt{3 x + 3 y}}$$
Pyramid 302
Preview $$U_{302}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}{3 \sqrt{x} \left(1 - y\right)^{2}}$$
Pyramid 303
Preview $$U_{303}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y} \left(1 - x\right)^{2}}$$
Pyramid 304
Preview $$U_{304}(x, y) = \frac{\sqrt{3} \sqrt{y} \left(x + \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y}\right)}{2 \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}$$
Pyramid 305
Preview $$U_{305}(x, y) = \frac{\sqrt{3} \left(1 - \sqrt{1 - 4 x}\right) \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 x \sqrt{y}}$$
Pyramid 306
Preview $$U_{306}(x, y) = - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{y \left(3 x - \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{\sqrt{y}}\right)}$$
Pyramid 307
Preview $$U_{307}(x, y) = \frac{\left(1 - \sqrt{1 - 4 x}\right) \left(1 - \sqrt{1 - 4 y}\right)}{4 x y}$$
Pyramid 308
Preview $$U_{308}(x, y) = - \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{y^{2} \left(4 x - \frac{2 - 2 \sqrt{1 - 4 y}}{y}\right)}$$
Pyramid 309
Preview $$U_{309}(x, y) = \frac{- 2 x y^{2} + 2 y + \sqrt{1 - 4 y} - 1}{y \left(\sqrt{1 - 4 y} - 1\right)}$$
Pyramid 310
Preview $$U_{310}(x, y) = \frac{2 y + \sqrt{1 - 4 y} - \sqrt{2} \sqrt{4 x y^{3} + 2 y^{2} - 4 y + \sqrt{1 - 4 y} \left(- 4 x y^{3} + 2 y - 1\right) + 1} - 1}{2 y \sqrt{1 - 4 y} - 2 y}$$
Pyramid 311
Preview $$U_{311}(x, y) = - \frac{1}{x y^{2} + x + y \left(1 - 2 x\right) - 1}$$
Pyramid 312
Preview $$U_{312}(x, y) = \frac{- x y^{2} + 2 x y - x - 1}{y - 1}$$
Pyramid 313
Preview $$U_{313}(x, y) = \frac{1}{\left(1 - x\right)^{2} \left(1 - y\right)^{2}}$$
Pyramid 314
Preview $$U_{314}(x, y) = x + \frac{\sqrt{\frac{4 x}{\left(1 - y\right)^{2}} + \frac{1}{\left(1 - y\right)^{4}}}}{2} + \frac{1}{2 \left(1 - y\right)^{2}}$$
Pyramid 315
Preview $$U_{315}(x, y) = x - \frac{\sqrt{\frac{4 x}{\left(1 - y\right)^{2}} + \frac{1}{\left(1 - y\right)^{4}}}}{2} + \frac{1}{2 \left(1 - y\right)^{2}}$$
Pyramid 316
Preview $$U_{316}(x, y) = \frac{1 - \sqrt{1 - 4 x}}{2 x \left(1 - y\right)^{2}}$$
Pyramid 317
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Preview $$U_{317}(x, y) = - \frac{1}{\left(1 - y\right)^{4} \left(x - \frac{1}{\left(1 - y\right)^{2}}\right)}$$
Pyramid 318
Preview $$U_{318}(x, y) = x \left(1 - y\right)^{2} + \frac{1}{\left(1 - y\right)^{2}}$$
Pyramid 319
Preview $$U_{319}(x, y) = \frac{\sqrt{4 x y^{6} - 24 x y^{5} + 60 x y^{4} - 80 x y^{3} + 60 x y^{2} - 24 x y + 4 x + 1} + 1}{2 y^{2} - 4 y + 2}$$
Pyramid 320
Preview $$U_{320}(x, y) = \frac{1 - \sqrt{4 x y^{6} - 24 x y^{5} + 60 x y^{4} - 80 x y^{3} + 60 x y^{2} - 24 x y + 4 x + 1}}{2 y^{2} - 4 y + 2}$$
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