1x1x1 Cube

The 1x1x1 Cube (also referred to as the 1x1x1 or 1x1) is a 'twistable puzzle' consisting of a single solitary cube or cubie.
The 1x1x1 cube has six different coloured uniform faces. Although often considered a joke (with numerous "solution guides" on YouTube), it does nevertheless exist. Some people make their own for fun, but in the 2010s it has also become available to purchase in many online cube stores. It is sometimes bought by cubers to complete the traditional standard cubes collection, so that they don't start at the 2x2x2 Cube.
Mathematics
Although relatively trivial, the mathematics of the 1x1x1 cube puzzle have been studied, usually in relation to the larger cubes as the simplest case available (ignoring the even simpler 0x0x0 Cube). God's Number is easily determined for the 1x1x1 cube, and God's Algorithm (the optimal solution to produce a required state) is easy to compute.
 Ignoring cube rotations, i.e. whole cube rotations are considered to be equivalent (as with the standard Rubik's Cube) then there is only one state, nothing can ever move, and the puzzle is always solved.
 If orientation of the cube is important, e.g. that one particular colour must be on top, then there are 6 distinct states of the cube. God's number is 1 in HTM and 2 in QTM.
 If one considers whole cube rotations to be distinct, then there are a total of 24 distinct states. God's number in this situation is is 2 in HTM and 3 in QTM.
Discussions:
 God's Algorithm for the 1x1x1 Rubik's Cube, Jerry Bryan, Cube Lovers, 14 November 1995
 Hamiltonian Circuit for a 1x1x1 cube, Discussion in 'Puzzle Theory' started by ortwin, February 7, 2016, Speedsolving Forums
See also
Regular cubic twisty puzzles  

Pocket Cube 
Rubik's Cube 
Rubik's Revenge  
Professor's Cube 
VCube 6 
VCube 7 
VCube 8 

SengSo 12x12 
MoYu 13x13 
SengSo 14x14  
MoYu 15x15 
Over The Top 
WuYa  
Massproduced  Exists, not manufactured  Work in progress 