I am only playing devil's advocate here, but according to this link, the word "polychotomous" does not exist, but I must be careful to say that it appears quite frequently in literature, which then raises the question, "Who is right?", or "two schools of thought"?
8.1 - Polytomous (Multinomial) Logistic Regression | STAT 504
https://onlinecourses.science.psu.edu/stat504/node/172We have already learned about binary logistic regression, where the ... (Note: The word polychotomous is sometimes used, but this word does not exist!).
Logistic Regression Models for Multinomial and Ordinal Variables
www.theanalysisfactor.com/logistic-regression-models-for-mu...The multinomial (a.k.a. polytomous) logistic regression model is a simple extension of the binomial logistic regression model. ... In multinomial logistic regression the dependent variable is dummy coded into multiple 1/0 variables. ... The mulitnomial logistic regression then estimates a ...
It could not be further from my working field, so I leave it at that. Regards.