Face two-colourable triangulations of $K_{13}$

Grannell, Mike; Griggs, Terry and Knor, M. (2003). Face two-colourable triangulations of $K_{13}$ . Journal of Combinatorial Mathematics and Combinatorial Computing, 47, pp. 75–81.

Abstract

Face two-colourable triangular embeddings of complete graphs $K_n$ correspond to biembeddings of Steiner triple systems. Such embeddings exist only if $n$ is congruent to $1$ or $3$ modulo $6$ . In this paper we present the number of these embeddings for $n=13$ .