The Government of Puerto Rico is a republican form of government with separation of powers, subject to the jurisdiction and sovereignty of the United States.
 of the Constitution of Puerto Rico defines the government and its political power and authority pursuant to U.S. Pub.L.
 82–447 .
 Said law mandated the establishment of a local constitution due to Puerto Rico's political status as a commonwealth of the United States.
 Ultimately, the powers of the government of Puerto Rico are all delegated by Congress and lack full protection under the U.S. Constitution.
 Because of this, the head of state of Puerto Rico is the President of the United States.
In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other.
 They are examples of topological invariants, which reflect, in algebraic terms, the structure of spheres viewed as topological spaces, forgetting about their precise geometry.
 Unlike homology groups, which are also topological invariants, the homotopy groups are surprisingly complex and difficult to compute.
The History of Roman and Byzantine domes traces the architecture of domes throughout the ancient Roman Empire and its medieval continuation, today called the Byzantine Empire.
 Domes were important architectural elements in both periods and had widespread influence on contemporary and later styles, from Russian and Ottoman architecture to the Italian Renaissance and modern revivals.
 The domes were customarily hemispherical, although octagonal and segmented shapes are also known, and they developed in form, use, and structure over the centuries.
 Early examples rested directly on the rotunda walls of round rooms and featured a central oculus for ventilation and light.
 Pendentives became common in the Byzantine period, provided support for domes over square spaces.
A geodesic dome is a hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron.
 The triangular elements of the dome are structurally rigid and distribute the structural stress throughout the structure, making geodesic domes able to withstand very heavy loads for their size.
Lloyd Hamilton Donnell (May 25, 1895 – November 7, 1997) was an American mechanical engineer, and Professor of Mechanical Engineering at the Illinois Institute of Technology.
 He is considered internationally renowned expert in engineering mechanics, specifically known for his work on shell analysis and thin-shell structure.
 He was recipient of the 1969 ASME Medal.
Triodetic dome is a partial dome structure that is similar but different from Geodesic dome in that it is not a full sphere.
Naruko (鳴子火山群 , "Naruko kazangun" ) is a stratovolcano located in Ōsaki, Miyagi Prefecture, Japan.
 The volcano consists of a 7 km wide caldera with several lava domes.
 The summit of the 461 m high Mt. Kurumigatake is one of the four lava domes located in the center of the caldera.
 The volcano is well known because of its relationship to the Naruko Hot Springs Villages.
 However, its lack of well-defined features makes it difficult to recognize for a casual observer.
 The Japan Metrological Agency considers Naruko to be an active volcano.
Isaac Newton's rotating spheres argument attempts to demonstrate that true rotational motion can be defined by observing the tension in the string joining two identical spheres.
 The basis of the argument is that all observers make two observations: the tension in the string joining the bodies (which is the same for all observers) and the rate of rotation of the spheres (which is different for observers with differing rates of rotation).
 Only for the truly non-rotating observer will the tension in the string be explained using only the observed rate of rotation.
 For all other observers a "correction" is required (a centrifugal force) that accounts for the tension calculated being different from the one expected using the observed rate of rotation.
 It is one of five arguments from the "properties, causes, and effects" of true motion and rest that support his contention that, in general, true motion and rest cannot be defined as special instances of motion or rest relative to other bodies, but instead can be defined only by reference to absolute space.
 Alternatively, these experiments provide an operational definition of what is meant by "absolute rotation", and do not pretend to address the question of "rotation relative to "what"?"
 General relativity dispenses with absolute space and with physics whose cause is external to the system, with the concept of geodesics of spacetime.
A "de facto" embassy is an office or organisation that serves "de facto" as an embassy in the absence of normal or official diplomatic relations among countries (thus paradiplomacy); usually, to represent nations which lack full diplomatic recognition, regions or dependencies of countries, or territories over which sovereignty is disputed.
 In some cases, diplomatic immunity and extraterritoriality may be granted.
The frog thermometer or - as the Cimento academicians defined it, the "botticino" [small-toad] thermometer - contained small glass spheres of different density, which were immersed in alcohol.
 The device was used as a clinical thermometer, tied to the wrist or the arm of the patient with the head of the frog facing upward.
 The variations in body temperature were registered by the movement of the spheres.
 The rise in temperature causes an increase in the volume of the alcohol, reflected in the movement of the small spheres (first the less dense, then the more dense).
 Because of the spheres' sluggish motion, this thermometer was also called infingardo [slothful, slow].
 The invention of this model is attributed to Ferdinand II de' Medici.

Question: Triodetic domes are different than what thin-shell structure in that they lack full spheres?
Answer: geodesic dome