Imaginary-order square tiling

An imaginary-order square tiling is a regular noncompact hyperbolic tiling with square faces and pseudogonal vertex figures.

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$\{4,2\}$	$\{4,3\}$	$\{4,4\}$	$\{4,5\}$	$\{4,6\}$	$\{4,7\}$	$\{4,8\}$	...	$\{4,\infty\}$	$\{4, \frac{\pi i}{\lambda}\}$
Square dihedron	Cube	Square tiling	Order-5 square tiling	Order-6 square tiling	Order-7 square tiling	Order-8 square tiling	...	Infinite-order square tiling	Imaginary-order square tiling


$\{2,\frac{\pi i}{\lambda}\}$	$\{3,\frac{\pi i}{\lambda}\}$	$\{4, \frac{\pi i}{\lambda}\}$	$\{5,\frac{\pi i}{\lambda}\}$	$\{6,\frac{\pi i}{\lambda}\}$	$\{7,\frac{\pi i}{\lambda}\}$	$\{8,\frac{\pi i}{\lambda}\}$	...	$\{\infty,\frac{\pi i}{\lambda}\}$	$\{\frac{\pi i}{\lambda_1},\frac{\pi i}{\lambda_2}\}$
Pseudogonal hosohedron	Imaginary-order triangular tiling	Imaginary-order square tiling	Imaginary-order pentagonal tiling	Imaginary-order hexagonal tiling	Imaginary-order heptagonal tiling	Imaginary-order octagonal tiling	...	Imaginary-order apeirogonal tiling	Imaginary-order pseudogonal tiling