I wanted to try a flat and fixed design again, because it can be much smaller and more robust (being transported in a bag with other items without special care) at the same time.
To decide on the geometry and to test whether I can bear an untented keyboard (yes, I can, but only if something more comfortable is not available) I built a flat keyboard from existing parts and some scrap wood:

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on a table
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on the lap while sitting on a chair (which includes on the bus or train)
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on the lap while sitting on a couch with outstretched legs
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every situation where you’d usually use a laptop’s keyboard, because it can be used on top of a laptop’s keyboard
The keyboard includes
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palmrests
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several smartphone mounts
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storage space
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a battery and can connect via bluetooth.
Keyboard on top of a laptop (13" screen):
Those three little darker discs at the left rear are two LEDs (charging indicator, status indicator) and a reset button.
The smartphone is held suprisingly well (even on a train or bus) which is why I didn’t include additional pins on the left and right of it, which where meant to keep it in place.
Smartphone at a steep angle:
Although the fairphone 4 is heavy and not at a steep angle here, the keyboard does not fall over: