Quantitative kurtosis phantoms are sought by multicenter clinical trials to establish accuracy and precision of quantitative imaging biomarkers on the basis of diffusion kurtosis imaging (DKI) parameters. We designed and evaluated precision, reproducibility, and long-term stability of a novel isotropic (i)DKI phantom fabricated using four families of chemicals based on vesicular and lamellar mesophases of liquid crystal materials. The constructed iDKI phantoms included negative control monoexponential diffusion materials to independently characterize noise and model-induced bias in quantitative kurtosis parameters. Ten test–retest DKI studies were performed on four scanners at three imaging centers over a six-month period. The tested prototype phantoms exhibited physiologically relevant apparent diffusion, D
app
, and kurtosis, K
app
, parameters ranging between 0.4 and 1.1 (×10
−3
mm
2
/s) and 0.8 and 1.7 (unitless), respectively. Measured kurtosis phantom K
app
exceeded maximum fit model bias (0.1) detected for negative control (zero kurtosis) materials. The material-specific parameter precision [95% CI for D
app
: 0.013–0.022(×10
−3
mm
2
/s) and for K
app
: 0.009–0.076] derived from the test–retest analysis was sufficient to characterize thermal and temporal stability of the prototype DKI phantom through correlation analysis of inter-scan variability. The present study confirms a promising chemical design for stable quantitative DKI phantom based on vesicular mesophase of liquid crystal materials. Improvements to phantom preparation and temperature monitoring procedures have potential to enhance precision and reproducibility for future multicenter iDKI phantom studies.