icosahedral_number

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full burden. It states the tool calculates a value, implying a read-only operation, but doesn't disclose any behavioral traits such as input validation (e.g., handling negative 'n'), performance characteristics, error conditions, or output format. For a tool with no annotation coverage, this leaves significant gaps in understanding its behavior.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is extremely concise and front-loaded: the first sentence states the core purpose, and the second adds domain/category context. There is no wasted text, and every sentence contributes directly to understanding the tool's function. It efficiently communicates the essential information without redundancy.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's low complexity (1 parameter, no output schema, no annotations), the description is minimally complete. It states what the tool does but lacks details on usage, behavior, and parameter semantics. For a simple calculator, this might suffice, but the absence of output information and behavioral context leaves room for improvement in helping an agent invoke it correctly.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has 1 parameter ('n') with 0% description coverage. The description adds no parameter-specific information beyond implying 'n' is an integer for the calculation. It doesn't explain what 'n' represents (e.g., index, order) or any constraints (e.g., non-negative). Given the low schema coverage, the description compensates minimally, meeting the baseline for adequate but incomplete documentation.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose: 'Calculate the nth icosahedral number.' It specifies the verb ('calculate') and resource ('icosahedral number'), and the domain/category context helps distinguish it from general arithmetic tools. However, it doesn't explicitly differentiate it from other figurate number tools like 'tetrahedral_number' or 'dodecahedral_number' in the sibling list.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('arithmetic') and category ('figurate_numbers'), which implies context, but doesn't specify use cases, prerequisites, or comparisons to sibling tools like 'polygonal_number' or other figurate number calculators. The agent must infer usage from the category alone.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.