Gluconeogenic capability of the cell is determined by the presence of
Fructose 1-6 biphosphatase 

Glyconeogenesis refers to the synthesis of glycogen from non-carbohydrate precursors like fat or proteins, without using glucose or other carbohydrates. It should not be confused with glycogenesis which refers to the synthesis of glycogen from glucose.
Process of glyconeogenesis is same as for gluconeogenesis except for the last step, where glucose-6-phosphate enters the glycogen synthesis cycle instead of conversion into glucose.
So, glyconeogenesis and gluconeogenesis are same processes.

"The conversion of fructose 1, 6-bisphosphate to fructose-6-phosphate, for the reversal of glycolysis, is catalyzed by fructose-1, 6-bisphosphatase. Its presence determines whether a tissue is capable of synthesizing glucose, i.e. gluconeogenesis (or glycogen, i.e., glyconeogenesis) not only from pyruvate but also from triose phosphates".
Pyruvate dehydrogenase
Glucose 6 phosphatase
Pyruvate carboxylase
Fructose 1–6 biphosphatase