Grand County is one of the 64 counties in the U. S. state of Colorado. As of the 2010 census, the population was 14,843; the county seat is Hot Sulphur Springs. When Grand County was created February 2, 1874 it was carved out of Summit County and contained land to the western and northern borders of the state, in present-day Moffat County and Routt County, it was named after Grand Lake and the Grand River, an old name for the upper Colorado River, which has its headwaters in the county. On January 29, 1877 Routt County was created and Grand County shrunk down to its current western boundary; when valuable minerals were found in North Park, Grand County claimed the area as part of its county, a claim Larimer County held. It took a decision by the Colorado Supreme Court in 1886 to declare North Park part of Larimer County, setting Grand County's northern boundary. According to the U. S. Census Bureau, the county has a total area of 1,870 square miles, of which 1,846 square miles is land and 23 square miles is water.

Great Parks Bicycle Route TransAmerica Trail Bicycle Route Colorado River Headwaters National Scenic Byway Trail Ridge Road/Beaver Meadow National Scenic Byway As of the census of 2000, there were 12,442 people, 5,075 households, 3,217 families residing in the county. The population density was 7 people per square mile. There were 10,894 housing units at an average density of 6 per square mile; the racial makeup of the county was 95.15% White, 0.48% Black or African American, 0.43% Native American, 0.68% Asian, 0.10% Pacific Islander, 2.00% from other races, 1.15% from two or more races. 4.36% of the population were Hispanic or Latino of any race. 23.8 % were of 10.0 % English and 7.3 % American ancestry. There were 5,075 households out of which 28.10% had children under the age of 18 living with them, 54.70% were married couples living together, 5.20% had a female householder with no husband present, 36.60% were non-families. 24.80% of all households were made up of individuals and 4.80% had someone living alone, 65 years of age or older.

The average household size was 2.37 and the average family size was 2.85. In the county, the population was spread out with 21.80% under the age of 18, 9.00% from 18 to 24, 34.70% from 25 to 44, 26.80% from 45 to 64, 7.80% who were 65 years of age or older. The median age was 37 years. For every 100 females there were 112.70 males. For every 100 females age 18 and over, there were 115.70 males. The median income for a household in the county was $47,759, the median income for a family was $55,217. Males had a median income of $34,861 versus $26,445 for females; the per capita income for the county was $25,198. About 5.40% of families and 7.30% of the population were below the poverty line, including 7.90% of those under age 18 and 6.10% of those age 65 or over. Fraser Granby Grand Lake Hot Sulphur Springs Kremmling Winter Park Parshall Tabernash Radium Colorado portal List of counties in Colorado Saratoga County, Jefferson Territory National Register of Historic Places listings in Grand County, Colorado Official website Arapaho National Recreation Area website Colorado County Evolution by Don Stanwyck Colorado Historical Society Grand County Library District website Grand County News website Grand County Tourism Board website Town of Hot Sulphur Springs website Rocky Mountain National Park website Winter Park and Fraser Valley Chamber of Commerce website Grand Lake Chamber of Commerce homepage WorkInGrand Portal

In eight-dimensional geometry, a heptellated 8-simplex is a convex uniform 8-polytope, including 7th-order truncations from the regular 8-simplex. There are 35 unique heptellations for the 8-simplex, including all permutations of truncations, runcinations, sterications and hexications; the simplest heptellated 8-simplex is called an expanded 8-simplex, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 8-simplex. The highest form, the heptihexipentisteriruncicantitruncated 8-simplex is more called a omnitruncated 8-simplex with all of the nodes ringed. Expanded 8-simplex Small exated enneazetton The vertices of the heptellated 8-simplex can bepositioned in 8-space as permutations of; this construction is based on facets of the heptellated 9-orthoplex. A second construction in 9-space, from the center of a rectified 9-orthoplex is given by coordinate permutations of: Its 72 vertices represent the root vectors of the simple Lie group A8; the symmetry order of an omnitruncated 9-simplex is 725760.

The symmetry of a family of a uniform polytopes is equal to the number of vertices of the omnitruncation, being 362880 in the case of the omnitruncated 8-simplex. Heptihexipentisteriruncicantitruncated 8-simplex Great exated enneazetton The Cartesian coordinates of the vertices of the omnitruncated 8-simplex can be most positioned in 9-space as permutations of; this construction is based on facets of the heptihexipentisteriruncicantitruncated 9-orthoplex, t0,1,2,3,4,5,6,7 The omnitruncated 8-simplex is the permutohedron of order 9. The omnitruncated 8-simplex is a zonotope, the Minkowski sum of nine line segments parallel to the nine lines through the origin and the nine vertices of the 8-simplex. Like all uniform omnitruncated n-simplices, the omnitruncated 8-simplex can tessellate space by itself, in this case 8-dimensional space with three facets around each ridge, it has Coxeter-Dynkin diagram of. This polytope is one of 135 uniform 8-polytopes with A8 symmetry. H. S. M. Coxeter: H. S. M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973 Kaleidoscopes: Selected Writings of H.

S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 H. S. M. Coxeter and Semi Regular Polytopes I, H. S. M. Coxeter and Semi-Regular Polytopes II, H. S. M. Coxeter and Semi-Regular Polytopes III, Norman Johnson Uniform Polytopes, Manuscript N. W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph. D. Klitzing, Richard. "8D uniform polytopes". X3o3o3o3o3o3o3x - soxeb, x3x3x3x3x3x3x3x - goxeb Polytopes of Various Dimensions Multi-dimensional Glossary

SYmbiosis Multitasking Based Operating System is a multitasking operating system for Zilog Z80-based 8-bit computer systems. Contrary to early 8-bit operating systems it is based on a microkernel, which provides preemptive and priority-oriented multitasking and manages random-access memory with a size of up to 1024 KB. SymbOS contains a Microsoft Windows like graphical user interface, supports hard disks with a capacity of up to 128 GB and can be booted on an unexpanded Amstrad CPC-6128, a 128K-MSX2 and an Amstrad PCW; as of August 30th 2017 it is available for the Amstrad CPC series of computers, all MSX models starting from the MSX2 standard, MSX with V9990 graphics chip, all Amstrad PCW models, CPC-TREX, C-ONE and the Enterprise 64/128 computers. SymbOS was started as an experiment to find out to what extent it is possible to implement a multitasking operating system with a windowed GUI on an 8-bit computer from 1985. GEOS contributed to the motivation, but the structure and features of SymbOS aren't similar to that system.

The release in 2006 proved that such a "mini windows" system is possible on a 20-year-old home computer with only quantitative limitations. SymbOS is one of the largest retro computing software projects of recent years. One of the goals of the project is to allow these old machines to be used like a modern PC, using hardware extensions. Although only an 8-bit CPU, the Z80 can run a preemptive multitasking operating system. Features such as memory protection, which the Z80 lacks, are not essential in such an OS. For example, AmigaOS lacks memory protection; the MP/M OS proved. Yet, it was unavailable for home computers. While the MOS Technology 6502 cannot move the stack pointer, the Z80 can relocate it to any position in memory, which makes it easier to implement preemptive multitasking; the existence of an alternative register set accelerates context switching between tasks dramatically. The restriction of Z80 system to a 64 KB address space can be solved with bank switching. In this way, computers like the Amstrad CPC and PCW, MSX, Enterprise or SAM Coupé can access hundreds or thousands of kilobytes of memory.

SymbOS includes a microkernel, which can perform task management, memory management and inter-process communication. For task management, a combination of preemptive and cooperative multitasking was chosen, which makes different task priorities possible. Preemptive means that tasks are interrupted after a certain amount of time by the operating system, in order to share the CPU time with other tasks. Cooperatively means, it does that, if it's waiting for a certain event. Because of this combination it is possible to assign priorities. Tasks with low priority get CPU time only if all tasks with higher priorities are not working. Memory management divides the entire RAM into small 256 byte blocks, which can be assigned dynamically. Applications are always running in a secondary 64 KB RAM bank, where no memory space is occupied by the operating system or the video memory; that makes it possible to reserve up to 63 KB in one piece. Banking management ensures that the system can administer memory with a size of up to one megabyte though the Z80 CPU has only a 16-bit address bus.

It makes transparent access to memory and functions placed in other 64 KB banks possible. Communication between different tasks and the operating system does not take place via calls, but is done via messages; this is necessary inside a multitasking environment to avoid organization problems with the stack, global variables and shared system resources. The SymbOS kernel supports synchronous and asynchronous IPC. SymbOS supports the file systems CP/M, AMSDOS, File Allocation Table 12-16-32, on all platforms. With the last one, SymbOS can address mass storage devices with a capacity of up to 128 GB; the ability to administer files with a size of up to 2 GB is uncommon for an 8-bit system. Because of the FAT support data exchange with other computers is quite easy, as most 32 and 64 bit operating systems do support the three FAT file systems; the graphical user interface of SymbOS works in a object-oriented manner. The look and feel mimics that of Microsoft Windows, it contains the well-known task bar with the clock and the "start" menu and can open up to 32 windows that can be moved and scrolled.

The whole system is written in optimized assembly language, meaning that the GUI runs as fast as the host machine supports. Content of a window is defined with "controls" that are primitive GUI elements such as sliders, check boxes, text lines, buttons or graphics; the background or invisible areas of a window don't need to be saved in a separate bitmap buffer. If an area needs to be restored on the display, its contents will be redrawn instead; this makes SymbOS GUI much more memory-friendly compared to most other 8-bit GUIs. There are several standard applications available for SymbOS, which most resemble their well-known Windows and Mac OS counterparts. Examples include SymCommander, SymShell, SymZilla, SymPlay, SymAmp and Minesweeper; the following list of commands is supported by SymShell. SymbOS was developed for the Amstrad CPC, its modular structure, with strict separation of general and hardware components, makes porting to other Z80-based systems comparatively easy. The MSX computers starting with the MSX2 standard have been supported since summer 2006.

The Amstrad PCW port has been available since August 2007. Versions for the Enterprise 128, the SAM Coupé and such clones of ZXSpectrum as ATM-turbo 2+ and ZX-Evolution/BaseConf are possible, too, as