No acute tetrahedron is an 8-reptile

No acute tetrahedron is an 8-reptile

An r-gentiling is a dissection of a shape into r ≥ 2 parts which are all similar to the original shape. An r-reptiling is an r-gentiling of which all parts are mutually congruent. This article shows that no acute tetrahedron is an r-gentile or r-reptile for any r < 9, by showing that no acute spherical diangle can be dissected into less than nine acute spherical triangles.

Observations from the 8-Tetrahedron Nonorientable Census

Through computer enumeration with the aid of topological results, we catalogue all 18 closed nonorientable P-irreducible 3-manifolds that can be formed from at most eight tetrahedra. In addition we give an overview as to how the 100 resulting minimal triangulations are constructed. Observations and conjectures are drawn from the census data, and future potential for the nonorientable census is ...

(An Analysis of Principle no.8 of the Constitution)

This article has analyzed principle no.8 of the Constitution from three aspects: 1-verbal analysis 2-conceptual analysis 3-ways to execute this principle. In first section a precise definition of "call to good", "good and evil" (both in law and in jurisprudence) and "government" have been presented. In second section to have a better understanding of principle no.8, issues such as the relation ...

Is CD19 an Immunological Diagnostic Marker for Acute Appendicitis?

Background: The appendix is considered as part of the gut-associated lymphoid tissue; however, lymphocyte subsets in this tissue are not fully defined. Objective: To investigate and compare the function and phenotype of lymphocyte subsets in peripheral blood and appendix of patients with normal and inflamed appendix tissues. Methods: Peripheral blood samples and appendiceal mononuclear cells we...

Vol. 8, No. 3 , 2019