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We describe the tangent cones at their j<\/jats:italic>-faces and compute explicitly the sums of the conic intrinsic volumes of these tangent cones at all j<\/jats:italic>-faces of $$K_n^A$$<\/jats:tex-math>\n \n K<\/mml:mi>\n n<\/mml:mi>\n A<\/mml:mi>\n <\/mml:msubsup>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and\u00a0$$K_n^B$$<\/jats:tex-math>\n \n K<\/mml:mi>\n n<\/mml:mi>\n B<\/mml:mi>\n <\/mml:msubsup>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. This setting contains sums of external and internal angles of $$K_n^A$$<\/jats:tex-math>\n \n K<\/mml:mi>\n n<\/mml:mi>\n A<\/mml:mi>\n <\/mml:msubsup>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and $$K_n^B$$<\/jats:tex-math>\n \n K<\/mml:mi>\n n<\/mml:mi>\n B<\/mml:mi>\n <\/mml:msubsup>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> as special cases. The sums are evaluated in terms of Stirling numbers of both kinds. We generalize these results to finite products of Schl\u00e4fli orthoschemes of type A<\/jats:italic> and B<\/jats:italic> and, as a probabilistic consequence, derive formulas for the expected number of j<\/jats:italic>-faces of the Minkowski sums of the convex hulls of a finite number of Gaussian random walks and random bridges. Furthermore, we evaluate the analogous angle sums for the tangent cones of Weyl chambers of types A<\/jats:italic> and B<\/jats:italic> and finite products thereof.<\/jats:p>","DOI":"10.1007\/s00454-021-00326-z","type":"journal-article","created":{"date-parts":[[2021,10,6]],"date-time":"2021-10-06T02:55:19Z","timestamp":1633488919000},"page":"125-164","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Angle Sums of Schl\u00e4fli Orthoschemes"],"prefix":"10.1007","volume":"68","author":[{"given":"Thomas","family":"Godland","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zakhar","family":"Kabluchko","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,10,5]]},"reference":[{"issue":"3","key":"326_CR1","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/BF02187839","volume":"7","author":"F Affentranger","year":"1992","unstructured":"Affentranger, F., Schneider, R.: Random projections of regular simplices. 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