The Geometry Descriptions of Crystallographic Groups of Sol

Abstract

The connected and simply connected four-dimensional matrix solvable Lie group $Sol^4_1$ 수식 이미지 is the four-dimensional geometry. A crystallographic group of $Sol^4_1$ 수식 이미지 is a discrete cocompact subgroup of $Sol^4_1{\rtimes}D(4)$ 수식 이미지. In this paper, we geometrically describe the crystallographic groups of $Sol^4_1$ 수식 이미지.