和英辞典で「一筆書き」を引くと、a picture drawn without lifting the brush from the paper とか出ていますが、これは「説明」であって、一筆書きに相当する「単語」ではありません。単語がないということは、一筆書きという概念がない、すなわち、一筆書きという遊びというかクイズというか、そういったものが英語文化圏にはないのでしょうか？
To draw a unicursal figure is defined by tracing all the part of the closed loop forming some kind of picture without taking a pen apart from a sheet of paper on which the picture is drawn. Additionally, you cannot retrace the line already traced.
The unicursal hexagram is a hexagram or six-pointed star that can be traced or drawn unicursally, in one continuous line rather than by two overlaid triangles. The hexagram can also be depicted inside a circle with the points touching it.
English author and occultist Aleister Crowley's adaptation of the unicursal hexagram placed a five petaled rose (symbolizing the Divine), in the center, the symbol as a whole making eleven (five petals of the rose plus six points of the hexagram), thought by some as the number of divine union. It is used in the Greek and Hindu mythologies as a symbol of dedication to the divine rulers.
A unicursal hexagram can also allegedly be seen as a symbol of the solar system in some Pagan philosophies, with the central intersection representing the sun and the outer intersections and points representing the celestial bodies.
 Popular culture
The unicursal hexagram was part of the symbol called "The Seal of Orichalcos" that was prominent in the Waking the Dragons arc of Yu-Gi-Oh! In fact, one of the antagonists of the arc is named Allister, referencing the famous occultist Aleister Crowley.
A unicursal hexagram appears several times in the television series Supernatural as a symbol to ward off evil entities.
Oni Sakti, Visual artist and memeber of the musical group Phantoms Of The SS has a unicursal hexagram tattooed on his right forearm.
Danny Carey, the drummer from the progressive metal band Tool, features the unicursal hexagram in some of his imagery and configures his drum kit more or less in this arrangement as well.
The members of Polish blackened death metal band Behemoth all wear pendants of unicursal hexagrams as part of their stage outfits.
The character Klytus, from the 1980 movie Flash Gordon, bears a unicursal hexagram on the front of his robes.