Abstract We consider the problem of embedding a symmetric configuration with block size 3 in an orientable surface in such a way that the blocks of the configuration form triangular faces and there is only one extra large face. We develop a sufficient condition for such an embedding to exist given any orientation of the configuration, and show that this condition is satisfied for all configurations on up to 19 points. We also show that there exists a configuration on 21 points which is not embeddable in any orientation. As a by-product, we give a revised table of numbers of configurations, correcting the published figure for 19 points. We give a number of open questions about embeddability of configurations on larger numbers of points.

中文翻译：

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关于块大小为 3 的对称配置的上嵌入

摘要 我们考虑在可定向表面中嵌入块大小为 3 的对称配置的问题，使得配置的块形成三角形面，并且只有一个特大面。我们开发了在给定配置的任何方向的情况下存在这种嵌入的充分条件，并表明该条件对于最多 19 个点的所有配置都满足。我们还表明，在 21 个点上存在一个配置，该配置不能以任何方向嵌入。作为副产品，我们给出了一个修改后的配置数量表，将公布的数字修正为 19 分。我们给出了许多关于配置在大量点上的可嵌入性的开放性问题。